How do you solve (x+3)(x+5) = -7?

1 Answer
Oct 27, 2015

x=-4+-isqrt(6)

Explanation:

You first need to make one side 0.

[1]" "(x+3)(x+5)=-7

Expand (x+3)(x+5).

[2]" "x^2+8x+15=-7

Add 7 to both sides.

[3]" "x^2+8x+15+7=-7+7

[4]" "x^2+8x+22=0

Now that you have equated everything to 0, you can solve for the roots. The roots of this quadratic equation are actually imaginary, so you should make use of the quadratic formula.

[5]" "x=(-b+-sqrt(b^2-4ac))/(2a)

[6]" "x=(-(8)+-sqrt((8)^2-4(1)(22)))/(2(1))

[7]" "x=(-8+-sqrt(64-88))/2

[8]" "x=(-8+-sqrt(-24))/2

[9]" "x=(-8+-2isqrt(6))/2

[10]" "color(blue)(x=-4+-isqrt(6))