Use the method of completing the square to solve the quadratic equation. x ( x + 10 ) = -7
A) $x = - 5 + 3 \sqrt { 2 } , x = 5 - 3 \sqrt { 2 }$
B) $x = 5 + 3 \sqrt { 2 } , x = 5 + 3 \sqrt { 2 }$
C) $x = - 5 + 3 \sqrt { 2 } , x = - 5 - 3 \sqrt { 2 }$

Question

Quizplus · Accepted Answer

First, expand the left side and collect like terms to get:

$x^2+10x+7=0$

Next, complete the square by adding $(10/2)^2=25$ to both sides:

$x^2+10x+25+7=25$

$(x+5)^2=18$

Take the square root of both sides:

$x+5=\pm\sqrt{18}$

$x=-5\pm3\sqrt{2}$

Therefore, the solution is x = - 5 + 3sqrt(2) or x = - 5 - 3sqrt(2).

Use the Method of Completing the Square to Solve the Quadratic