x^2-56x+167=4365

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Solution for x^2-56x+167=4365 equation:


Simplifying
x2 + -56x + 167 = 4365

Reorder the terms:
167 + -56x + x2 = 4365

Solving
167 + -56x + x2 = 4365

Solving for variable 'x'.

Reorder the terms:
167 + -4365 + -56x + x2 = 4365 + -4365

Combine like terms: 167 + -4365 = -4198
-4198 + -56x + x2 = 4365 + -4365

Combine like terms: 4365 + -4365 = 0
-4198 + -56x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4198' to each side of the equation.
-4198 + -56x + 4198 + x2 = 0 + 4198

Reorder the terms:
-4198 + 4198 + -56x + x2 = 0 + 4198

Combine like terms: -4198 + 4198 = 0
0 + -56x + x2 = 0 + 4198
-56x + x2 = 0 + 4198

Combine like terms: 0 + 4198 = 4198
-56x + x2 = 4198

The x term is -56x.  Take half its coefficient (-28).
Square it (784) and add it to both sides.

Add '784' to each side of the equation.
-56x + 784 + x2 = 4198 + 784

Reorder the terms:
784 + -56x + x2 = 4198 + 784

Combine like terms: 4198 + 784 = 4982
784 + -56x + x2 = 4982

Factor a perfect square on the left side:
(x + -28)(x + -28) = 4982

Calculate the square root of the right side: 70.58328414

Break this problem into two subproblems by setting 
(x + -28) equal to 70.58328414 and -70.58328414.


Subproblem 1
x + -28 = 70.58328414

Simplifying
x + -28 = 70.58328414

Reorder the terms:
-28 + x = 70.58328414

Solving
-28 + x = 70.58328414

Solving for variable 'x'.

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

Add '28' to each side of the equation.
-28 + 28 + x = 70.58328414 + 28

Combine like terms: -28 + 28 = 0
0 + x = 70.58328414 + 28
x = 70.58328414 + 28

Combine like terms: 70.58328414 + 28 = 98.58328414
x = 98.58328414

Simplifying
x = 98.58328414


Subproblem 2
x + -28 = -70.58328414

Simplifying
x + -28 = -70.58328414

Reorder the terms:
-28 + x = -70.58328414

Solving
-28 + x = -70.58328414

Solving for variable 'x'.

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

Add '28' to each side of the equation.
-28 + 28 + x = -70.58328414 + 28

Combine like terms: -28 + 28 = 0
0 + x = -70.58328414 + 28
x = -70.58328414 + 28

Combine like terms: -70.58328414 + 28 = -42.58328414
x = -42.58328414

Simplifying
x = -42.58328414


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {98.58328414, -42.58328414}

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