# How do you solve sqrt(x^2+9x+15)=x+5 and check your solution?

Feb 27, 2017

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#### Explanation:

Square both sides:

${\left(\sqrt{{x}^{2} + 9 x + 15}\right)}^{2} = {\left(x + 5\right)}^{2}$

${x}^{2} + 9 x + 15 = {x}^{2} + 10 x + 25$

${x}^{2} - {x}^{2} + 9 x - 10 x + 15 - 25 = 0$

$- x - 10 = 0$

$x = - 10$

Check:

sqrt((-10)^2 + 9(-10) + 15) =^? -10 + 5

$\sqrt{25} \ne - 5$

There is no solution to this equation.

Hopefully this helps!