5x=(18+x)(18+x)

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Solution for 5x=(18+x)(18+x) equation: 


Simplifying
5x = (18 + x)(18 + x)

Multiply (18 + x) * (18 + x)
5x = (18(18 + x) + x(18 + x))
5x = ((18 * 18 + x * 18) + x(18 + x))
5x = ((324 + 18x) + x(18 + x))
5x = (324 + 18x + (18 * x + x * x))
5x = (324 + 18x + (18x + x2))

Combine like terms: 18x + 18x = 36x
5x = (324 + 36x + x2)

Solving
5x = 324 + 36x + x2

Solving for variable 'x'.

Reorder the terms:
-324 + 5x + -36x + -1x2 = 324 + 36x + x2 + -324 + -36x + -1x2

Combine like terms: 5x + -36x = -31x
-324 + -31x + -1x2 = 324 + 36x + x2 + -324 + -36x + -1x2

Reorder the terms:
-324 + -31x + -1x2 = 324 + -324 + 36x + -36x + x2 + -1x2

Combine like terms: 324 + -324 = 0
-324 + -31x + -1x2 = 0 + 36x + -36x + x2 + -1x2
-324 + -31x + -1x2 = 36x + -36x + x2 + -1x2

Combine like terms: 36x + -36x = 0
-324 + -31x + -1x2 = 0 + x2 + -1x2
-324 + -31x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-324 + -31x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(324 + 31x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(324 + 31x + x2)' equal to zero and attempt to solve:

Simplifying
324 + 31x + x2 = 0

Solving
324 + 31x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-324' to each side of the equation.
324 + 31x + -324 + x2 = 0 + -324

Reorder the terms:
324 + -324 + 31x + x2 = 0 + -324

Combine like terms: 324 + -324 = 0
0 + 31x + x2 = 0 + -324
31x + x2 = 0 + -324

Combine like terms: 0 + -324 = -324
31x + x2 = -324

The x term is 31x.  Take half its coefficient (15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
31x + 240.25 + x2 = -324 + 240.25

Reorder the terms:
240.25 + 31x + x2 = -324 + 240.25

Combine like terms: -324 + 240.25 = -83.75
240.25 + 31x + x2 = -83.75

Factor a perfect square on the left side:
(x + 15.5)(x + 15.5) = -83.75

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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