# Solve the Quadratic equation by factorization x^{2}-5x-24=0

Solve the Quadratic equation by factorization
${x}^{2}-5x-24=0$
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Step 1
given that, ${x}^{2}-5x-24=0$
we have to solve the quadratic equation by factorization
Step 2
here, we using the splitting method to factorize the quadratic equation
in order to factorize, ${x}^{2}-5x-24=0$, we find two numbers p and q such that
p-q=5 and $p×q=24$.
clearly, 8-3=5, $8×3=24$
now we split the middle term
${x}^{2}-5x-24=0$
$⇒{x}^{2}-\left(8-3\right)x-24=0$
$⇒{x}^{2}-8x+3x-24=0$
$⇒x\left(x-8\right)+3\left(x-8\right)=0$
$⇒\left(x-8\right)\left(x+3\right)=0$
$⇒x-8=0,x+3=0$
$⇒x=8,x=-3$

Timothy Wolff
Step 1 Given
${x}^{2}-5x-24=0$
Step 2 Solving
${x}^{2}-8x+3x-24$
x(x-8)+3(x-8)
(x-8)(x+3)=0
x-8=0, x+3=0
x=8; x=-3
$\therefore x=8,-3$