(x+3)(x+5)=-7

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Solution for (x+3)(x+5)=-7 equation:


Simplifying
(x + 3)(x + 5) = -7

Reorder the terms:
(3 + x)(x + 5) = -7

Reorder the terms:
(3 + x)(5 + x) = -7

Multiply (3 + x) * (5 + x)
(3(5 + x) + x(5 + x)) = -7
((5 * 3 + x * 3) + x(5 + x)) = -7
((15 + 3x) + x(5 + x)) = -7
(15 + 3x + (5 * x + x * x)) = -7
(15 + 3x + (5x + x2)) = -7

Combine like terms: 3x + 5x = 8x
(15 + 8x + x2) = -7

Solving
15 + 8x + x2 = -7

Solving for variable 'x'.

Reorder the terms:
15 + 7 + 8x + x2 = -7 + 7

Combine like terms: 15 + 7 = 22
22 + 8x + x2 = -7 + 7

Combine like terms: -7 + 7 = 0
22 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + 8x + -22 + x2 = 0 + -22

Reorder the terms:
22 + -22 + 8x + x2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 8x + x2 = 0 + -22
8x + x2 = 0 + -22

Combine like terms: 0 + -22 = -22
8x + x2 = -22

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -22 + 16

Reorder the terms:
16 + 8x + x2 = -22 + 16

Combine like terms: -22 + 16 = -6
16 + 8x + x2 = -6

Factor a perfect square on the left side:
(x + 4)(x + 4) = -6

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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