Question

Solve the equation by completing the square. Round to the nearest hundredth. X^2 + 6x = -7

Answer 1

The given expression is:

$x^{2} +6x=-7 \\ \\ x^{2} +2(x)(3)=-7$

Adding the square of 3 to both sides, to make the left hand side of the equation a complete square, we get:

$x^{2} +2(x)(3)+ 3^{2}=-7+ 3^{2} \\ \\ (x+3)^{2}=2 \\ \\ x+3=+- \sqrt{2}$

So the values of x are:

a) $x= \sqrt{2} - 3 = -1.59$

b) $x= -\sqrt{2} - 3 = -4.41$