(2x+5)(2x+5)=-7

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Solution for (2x+5)(2x+5)=-7 equation: 


Simplifying
(2x + 5)(2x + 5) = -7

Reorder the terms:
(5 + 2x)(2x + 5) = -7

Reorder the terms:
(5 + 2x)(5 + 2x) = -7

Multiply (5 + 2x) * (5 + 2x)
(5(5 + 2x) + 2x * (5 + 2x)) = -7
((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = -7
((25 + 10x) + 2x * (5 + 2x)) = -7
(25 + 10x + (5 * 2x + 2x * 2x)) = -7
(25 + 10x + (10x + 4x2)) = -7

Combine like terms: 10x + 10x = 20x
(25 + 20x + 4x2) = -7

Solving
25 + 20x + 4x2 = -7

Solving for variable 'x'.

Reorder the terms:
25 + 7 + 20x + 4x2 = -7 + 7

Combine like terms: 25 + 7 = 32
32 + 20x + 4x2 = -7 + 7

Combine like terms: -7 + 7 = 0
32 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 5x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
8 + 5x + x2 = 0

Solving
8 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 5x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 5x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5x + x2 = 0 + -8
5x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
5x + x2 = -8

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -8 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -8 + 6.25

Combine like terms: -8 + 6.25 = -1.75
6.25 + 5x + x2 = -1.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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