Question

0of%20%24x%24%20such%20that%20%24x%5E2%20%2B%2010x%20%2B%2025%20%3D%208%24." id="TexFormula1" title="Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$." alt="Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$." align="absmiddle" class="latex-formula">

Answer 1

Answer:

$x =-5\ - \sqrt{8}$

Step-by-step explanation:

Given

$x^2 + 10x + 25 = 8$

Required

Find the smallest value of x

$x^2 + 10x + 25 = 8$

Expand the expression on the right hand side

$x^2 + 5x + 5x + 25 = 8$

Factorize

$x(x+5)+5(x+5) = 8$

$(x+5)(x+5) = 8$

$(x+5)^2 = 8$

Take Square root of both sides

$\sqrt{(x+5)^2} = \±\sqrt{8}$

$(x+5) = \±\sqrt{8}$

Remove bracket

$x+5 = \±\sqrt{8}$

Subtract 5 from both sides

$x+5-5 =-5\± \sqrt{8}$

$x =-5\± \sqrt{8}$

$x =-5\ + \sqrt{8}$ or $x =-5\ - \sqrt{8}$

Comparing both values of x;

The smallest value of x is

$x =-5\ - \sqrt{8}$