Your question

Solve the quadratic equation x² − 5x + 6 = 0

MathematicsQuadratic EquationsFactorisation MethodDifficulty: EasySolve for xDemo sample

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Identify the equation

We have a quadratic in the standard form ax² + bx + c = 0 with a = 1, b = −5, c = 6.

ax² + bx + c = 0

Let us start by comparing the given equation with the standard form ax squared plus bx plus c equals zero.

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Step-by-step solution

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1
Identify the equation
We have a quadratic in the standard form ax² + bx + c = 0 with a = 1, b = −5, c = 6.
ax² + bx + c = 0
Reasoning: Recognising the form tells us we can factorise or use the quadratic formula.
💡 Important: Always compare with the standard form before solving.
2
Find two numbers that multiply to c and add to b
We need two numbers whose product is 6 (the value of c) and whose sum is −5 (the value of b).
product = 6, sum = −5
3
Split the middle term
Rewrite −5x as −2x − 3x using the numbers we found.
x² − 2x − 3x + 6 = 0
4
Factor by grouping
Group the first two and last two terms and take out common factors.
x(x − 2) − 3(x − 2) = 0 ⇒ (x − 2)(x − 3) = 0
5
Solve for x
A product equals zero when either factor is zero, so x − 2 = 0 or x − 3 = 0.
x = 2 or x = 3

Final answer

x = 2 or x = 3