Question

Which of the following are solutions to the equation below? Check all that apply x^2+10x+25=8

Answer 1

For this case we have the following equation:

$x ^ 2 + 10x + 25 = 8\\x ^ 2 + 10x + 25-8 = 0\\x ^ 2 + 10x + 17 = 0$

We apply the quadratic formula:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}$

In this case we have:$a = 1\\b = 10\\c = 17$

Substituting we have:

$x = \frac {-10 \pm \sqrt {10 ^ 2-4 (1) (17)}} {2 (1)}\\x = \frac {-10 \pm \sqrt {100-68}} {2}\\x = \frac {-10 \pm \sqrt {32}} {2}\\x = \frac {-10 \pm \sqrt {4 ^ 2 * 2}} {2}\\x = \frac {-10 \pm4 \sqrt {2}} {2}$

We have two solutions:

$x_ {1} = - 5 + 2 \sqrt {2}\\x_ {2} = - 5-2 \sqrt {2}$

Answer:

Option D, E