Question

solve the equation by factoring:
x^2 + 40x + 14x = 0

Answer 1

Step-by-step explanation:

${\red{\underline{\underline{\bold{Given:-}}}}}$

• The quadratic equation :- x² + 40 + 14x = 0

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The value of x by factorization.

${\green{\underline{\underline{\bold{Solution:-}}}}}$

$\tt\orange{By\:splitting \:the\:middle \:term}$

${x}^{2} + 14x + 40 \\ \\ 10x + 4x = 14x \: \: \: and \: \: 10 \times 4 = 40 \\ \\ \implies {x}^{2} + 10x + 4x + 40 = 0 \\ \\ \implies x(x + 10) + 4(x + 10) = 0 \\ \\ \implies(x + 10)(x + 4) = 0 \\ \\ \implies (x + 10) = 0 \: \: \: (or) \: \: \: (x + 4) = 0$

_______________

$(x + 10) = 0 \\ \\ \implies x + 10 = 0 \\ \\ \implies x = - 10$

________________

$(x + 4) = 0 \\ \\ \implies x + 4 = 0 \\ \\ \implies x = - 4$

$\large\purple{\underline{{\boxed{\textbf{ x = -10 ,\: -4}}}}}$