x^2-14x=57

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Solution for x^2-14x=57 equation: 


Simplifying
x2 + -14x = 57

Reorder the terms:
-14x + x2 = 57

Solving
-14x + x2 = 57

Solving for variable 'x'.

Reorder the terms:
-57 + -14x + x2 = 57 + -57

Combine like terms: 57 + -57 = 0
-57 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + -14x + 57 + x2 = 0 + 57

Reorder the terms:
-57 + 57 + -14x + x2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + -14x + x2 = 0 + 57
-14x + x2 = 0 + 57

Combine like terms: 0 + 57 = 57
-14x + x2 = 57

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 57 + 49

Reorder the terms:
49 + -14x + x2 = 57 + 49

Combine like terms: 57 + 49 = 106
49 + -14x + x2 = 106

Factor a perfect square on the left side:
(x + -7)(x + -7) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + -7) equal to 10.295630141 and -10.295630141.


Subproblem 1
x + -7 = 10.295630141

Simplifying
x + -7 = 10.295630141

Reorder the terms:
-7 + x = 10.295630141

Solving
-7 + x = 10.295630141

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 10.295630141 + 7

Combine like terms: -7 + 7 = 0
0 + x = 10.295630141 + 7
x = 10.295630141 + 7

Combine like terms: 10.295630141 + 7 = 17.295630141
x = 17.295630141

Simplifying
x = 17.295630141


Subproblem 2
x + -7 = -10.295630141

Simplifying
x + -7 = -10.295630141

Reorder the terms:
-7 + x = -10.295630141

Solving
-7 + x = -10.295630141

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -10.295630141 + 7

Combine like terms: -7 + 7 = 0
0 + x = -10.295630141 + 7
x = -10.295630141 + 7

Combine like terms: -10.295630141 + 7 = -3.295630141
x = -3.295630141

Simplifying
x = -3.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.295630141, -3.295630141}

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