x(x-27)+127=0

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Solution for x(x-27)+127=0 equation:


Simplifying
x(x + -27) + 127 = 0

Reorder the terms:
x(-27 + x) + 127 = 0
(-27 * x + x * x) + 127 = 0
(-27x + x2) + 127 = 0

Reorder the terms:
127 + -27x + x2 = 0

Solving
127 + -27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-127' to each side of the equation.
127 + -27x + -127 + x2 = 0 + -127

Reorder the terms:
127 + -127 + -27x + x2 = 0 + -127

Combine like terms: 127 + -127 = 0
0 + -27x + x2 = 0 + -127
-27x + x2 = 0 + -127

Combine like terms: 0 + -127 = -127
-27x + x2 = -127

The x term is -27x.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27x + 182.25 + x2 = -127 + 182.25

Reorder the terms:
182.25 + -27x + x2 = -127 + 182.25

Combine like terms: -127 + 182.25 = 55.25
182.25 + -27x + x2 = 55.25

Factor a perfect square on the left side:
(x + -13.5)(x + -13.5) = 55.25

Calculate the square root of the right side: 7.433034374

Break this problem into two subproblems by setting 
(x + -13.5) equal to 7.433034374 and -7.433034374.

Subproblem 1

x + -13.5 = 7.433034374 Simplifying x + -13.5 = 7.433034374 Reorder the terms: -13.5 + x = 7.433034374 Solving -13.5 + x = 7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 7.433034374 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 7.433034374 + 13.5 x = 7.433034374 + 13.5 Combine like terms: 7.433034374 + 13.5 = 20.933034374 x = 20.933034374 Simplifying x = 20.933034374

Subproblem 2

x + -13.5 = -7.433034374 Simplifying x + -13.5 = -7.433034374 Reorder the terms: -13.5 + x = -7.433034374 Solving -13.5 + x = -7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -7.433034374 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -7.433034374 + 13.5 x = -7.433034374 + 13.5 Combine like terms: -7.433034374 + 13.5 = 6.066965626 x = 6.066965626 Simplifying x = 6.066965626

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.933034374, 6.066965626}

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