Built for CBSE Class 10

One problem.Many ways.

Compare every valid path, understand what makes each one work, and find the method that feels made for you.

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3 routes found · Answer verified

Ways to solve

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01BEST ROUTE

Factorisation

Split the middle term using −2 and −3.

(x - 2)(x - 3) = 0 \to x = 2, 3

⚡ Fastest🧒 Easiest🎯 Board best

Walk through 5 steps

01
$x^2 - 5x + 6 = 0$
Find two numbers whose product is 6 and sum is −5.
02
$x^2 - 2x - 3x + 6 = 0$
Split the middle term using −2 and −3.
03
$x(x - 2) - 3(x - 2) = 0$
Group the first two and last two terms.
04
$(x - 2)(x - 3) = 0$
Take the common binomial factor.
05
$x = 2 \quad \text{or} \quad x = 3$
Apply the zero-product rule.

Why use it

Best when the quadratic has clean integer factors.

Common trap

Choose factor signs whose sum is −5, not +5.

02SAFEST

Quadratic formula

Use a = 1, b = −5 and c = 6 in the standard formula.

x = \frac{5 \pm \sqrt{25 - 24}}{2} \to x = 2, 3

🛡 Universal5 steps

Walk through 5 steps

01
$a = 1, \quad b = -5, \quad c = 6$
Read a, b and c from the standard form.
02
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Write the quadratic formula before substituting.
03
$x = \frac{5 \pm \sqrt{25 - 24}}{2}$
Substitute the coefficients carefully.
04
$x = \frac{5 \pm 1}{2}$
Simplify the discriminant.
05
$x = 2 \quad \text{or} \quad x = 3$
Evaluate both the plus and minus cases.

Why use it

A dependable route for every quadratic equation.

Common trap

Because b = −5, the numerator starts with −b = +5.

03CONCEPT PICK

Completing the square

Turn the expression into a perfect-square equation.

(x - 2.5)^2 = 0.25 \to x = 2, 3

🧠 Concept best5 steps

Walk through 5 steps

01
$x^2 - 5x = -6$
Move the constant term to the right.
02
$x^2 - 5x + \frac{25}{4} = \frac{1}{4}$
Add (−5 ÷ 2)² to both sides.
03
$\left(x - \frac{5}{2}\right)^2 = \frac{1}{4}$
Rewrite the left side as a perfect square.
04
$x - \frac{5}{2} = \pm \frac{1}{2}$
Take square roots on both sides.
05
$x = 2 \quad \text{or} \quad x = 3$
Solve the two linear equations.

Why use it

Best for understanding how the quadratic shifts into a square.

Common trap

Add the same value to both sides of the equation.

Your best route · three

Factorisation

Clean integer factors make this the shortest, most exam-friendly route.

Why this route?

Exam tip

Show the zero-product step before writing both roots. That small line protects the method mark.

Route lab

Compare methods

Scores · 1–5

Method	Speed	Easy	Board	Safe	Concept
Factorisation	5	5	5	4	4
Quadratic formula	3	4	5	5	4
Completing the square	2	3	3	3	5

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Mapping the cleanest route…

YYogiMath X

Built for CBSE Class 10

One problem.Many ways.

Compare every valid path, understand what makes each one work, and find the method that feels made for you.

Enter your maths

Build your expression

Type normally or tap a symbol below.

Loading math input…

Try an example

Answers verified Smart method ranking No fake methods

3 routes found · Answer verified

Ways to solve

Compare methods

01BEST ROUTE

Factorisation

Split the middle term using −2 and −3.

(x - 2)(x - 3) = 0 \to x = 2, 3

⚡ Fastest🧒 Easiest🎯 Board best

Walk through 5 steps

01
$x^2 - 5x + 6 = 0$
Find two numbers whose product is 6 and sum is −5.
02
$x^2 - 2x - 3x + 6 = 0$
Split the middle term using −2 and −3.
03
$x(x - 2) - 3(x - 2) = 0$
Group the first two and last two terms.
04
$(x - 2)(x - 3) = 0$
Take the common binomial factor.
05
$x = 2 \quad \text{or} \quad x = 3$
Apply the zero-product rule.

Why use it

Best when the quadratic has clean integer factors.

Common trap

Choose factor signs whose sum is −5, not +5.

02SAFEST

Quadratic formula

Use a = 1, b = −5 and c = 6 in the standard formula.

x = \frac{5 \pm \sqrt{25 - 24}}{2} \to x = 2, 3

🛡 Universal5 steps

Walk through 5 steps

01
$a = 1, \quad b = -5, \quad c = 6$
Read a, b and c from the standard form.
02
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Write the quadratic formula before substituting.
03
$x = \frac{5 \pm \sqrt{25 - 24}}{2}$
Substitute the coefficients carefully.
04
$x = \frac{5 \pm 1}{2}$
Simplify the discriminant.
05
$x = 2 \quad \text{or} \quad x = 3$
Evaluate both the plus and minus cases.

Why use it

A dependable route for every quadratic equation.

Common trap

Because b = −5, the numerator starts with −b = +5.

03CONCEPT PICK

Completing the square

Turn the expression into a perfect-square equation.

(x - 2.5)^2 = 0.25 \to x = 2, 3

🧠 Concept best5 steps

Walk through 5 steps

01
$x^2 - 5x = -6$
Move the constant term to the right.
02
$x^2 - 5x + \frac{25}{4} = \frac{1}{4}$
Add (−5 ÷ 2)² to both sides.
03
$\left(x - \frac{5}{2}\right)^2 = \frac{1}{4}$
Rewrite the left side as a perfect square.
04
$x - \frac{5}{2} = \pm \frac{1}{2}$
Take square roots on both sides.
05
$x = 2 \quad \text{or} \quad x = 3$
Solve the two linear equations.

Why use it

Best for understanding how the quadratic shifts into a square.

Common trap

Add the same value to both sides of the equation.

Your best route · three

Factorisation

Clean integer factors make this the shortest, most exam-friendly route.

Why this route?

Exam tip

Show the zero-product step before writing both roots. That small line protects the method mark.

Route lab

Compare methods

Scores · 1–5

Method	Speed	Easy	Board	Safe	Concept
Factorisation	5	5	5	4	4
Quadratic formula	3	4	5	5	4
Completing the square	2	3	3	3	5

Ask about this solution

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