3x-11=(x+5)(x+5)

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Solution for 3x-11=(x+5)(x+5) equation: 


Simplifying
3x + -11 = (x + 5)(x + 5)

Reorder the terms:
-11 + 3x = (x + 5)(x + 5)

Reorder the terms:
-11 + 3x = (5 + x)(x + 5)

Reorder the terms:
-11 + 3x = (5 + x)(5 + x)

Multiply (5 + x) * (5 + x)
-11 + 3x = (5(5 + x) + x(5 + x))
-11 + 3x = ((5 * 5 + x * 5) + x(5 + x))
-11 + 3x = ((25 + 5x) + x(5 + x))
-11 + 3x = (25 + 5x + (5 * x + x * x))
-11 + 3x = (25 + 5x + (5x + x2))

Combine like terms: 5x + 5x = 10x
-11 + 3x = (25 + 10x + x2)

Solving
-11 + 3x = 25 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
-11 + -25 + 3x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: -11 + -25 = -36
-36 + 3x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 3x + -10x = -7x
-36 + -7x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Reorder the terms:
-36 + -7x + -1x2 = 25 + -25 + 10x + -10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-36 + -7x + -1x2 = 0 + 10x + -10x + x2 + -1x2
-36 + -7x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-36 + -7x + -1x2 = 0 + x2 + -1x2
-36 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + -7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(36 + 7x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(36 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
36 + 7x + x2 = 0

Solving
36 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 7x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + 7x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 7x + x2 = 0 + -36
7x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
7x + x2 = -36

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -36 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -36 + 12.25

Combine like terms: -36 + 12.25 = -23.75
12.25 + 7x + x2 = -23.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = -23.75

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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