x^2-53x=288

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Solution for x^2-53x=288 equation: 


Simplifying
x2 + -53x = 288

Reorder the terms:
-53x + x2 = 288

Solving
-53x + x2 = 288

Solving for variable 'x'.

Reorder the terms:
-288 + -53x + x2 = 288 + -288

Combine like terms: 288 + -288 = 0
-288 + -53x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '288' to each side of the equation.
-288 + -53x + 288 + x2 = 0 + 288

Reorder the terms:
-288 + 288 + -53x + x2 = 0 + 288

Combine like terms: -288 + 288 = 0
0 + -53x + x2 = 0 + 288
-53x + x2 = 0 + 288

Combine like terms: 0 + 288 = 288
-53x + x2 = 288

The x term is -53x.  Take half its coefficient (-26.5).
Square it (702.25) and add it to both sides.

Add '702.25' to each side of the equation.
-53x + 702.25 + x2 = 288 + 702.25

Reorder the terms:
702.25 + -53x + x2 = 288 + 702.25

Combine like terms: 288 + 702.25 = 990.25
702.25 + -53x + x2 = 990.25

Factor a perfect square on the left side:
(x + -26.5)(x + -26.5) = 990.25

Calculate the square root of the right side: 31.468237955

Break this problem into two subproblems by setting 
(x + -26.5) equal to 31.468237955 and -31.468237955.


Subproblem 1
x + -26.5 = 31.468237955

Simplifying
x + -26.5 = 31.468237955

Reorder the terms:
-26.5 + x = 31.468237955

Solving
-26.5 + x = 31.468237955

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '26.5' to each side of the equation.
-26.5 + 26.5 + x = 31.468237955 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = 31.468237955 + 26.5
x = 31.468237955 + 26.5

Combine like terms: 31.468237955 + 26.5 = 57.968237955
x = 57.968237955

Simplifying
x = 57.968237955


Subproblem 2
x + -26.5 = -31.468237955

Simplifying
x + -26.5 = -31.468237955

Reorder the terms:
-26.5 + x = -31.468237955

Solving
-26.5 + x = -31.468237955

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '26.5' to each side of the equation.
-26.5 + 26.5 + x = -31.468237955 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = -31.468237955 + 26.5
x = -31.468237955 + 26.5

Combine like terms: -31.468237955 + 26.5 = -4.968237955
x = -4.968237955

Simplifying
x = -4.968237955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {57.968237955, -4.968237955}

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