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

1 Answer
Rafael
Oct 27, 2015

x=-4+-isqrt(6)x=−4±i√6

Explanation:

You first need to make one side 00.

[1]" "(x+3)(x+5)=-7[1] (x+3)(x+5)=−7

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

[2]" "x^2+8x+15=-7[2] x2+8x+15=−7

Add 77 to both sides.

[3]" "x^2+8x+15+7=-7+7[3] x2+8x+15+7=−7+7

[4]" "x^2+8x+22=0[4] x2+8x+22=0

Now that you have equated everything to 00, 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)[5] x=−b±√b2−4ac2a

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

[7]" "x=(-8+-sqrt(64-88))/2[7] x=−8±√64−882

[8]" "x=(-8+-sqrt(-24))/2[8] x=−8±√−242

[9]" "x=(-8+-2isqrt(6))/2[9] x=−8±2i√62

[10]" "color(blue)(x=-4+-isqrt(6))[10] x=−4±i√6

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