x^2-1351.9x=-56.9

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Solution for x^2-1351.9x=-56.9 equation: 


Simplifying
x2 + -1351.9x = -56.9

Reorder the terms:
-1351.9x + x2 = -56.9

Solving
-1351.9x + x2 = -56.9

Solving for variable 'x'.

Reorder the terms:
56.9 + -1351.9x + x2 = -56.9 + 56.9

Combine like terms: -56.9 + 56.9 = 0.0
56.9 + -1351.9x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '-56.9' to each side of the equation.
56.9 + -1351.9x + -56.9 + x2 = 0.0 + -56.9

Reorder the terms:
56.9 + -56.9 + -1351.9x + x2 = 0.0 + -56.9

Combine like terms: 56.9 + -56.9 = 0.0
0.0 + -1351.9x + x2 = 0.0 + -56.9
-1351.9x + x2 = 0.0 + -56.9

Combine like terms: 0.0 + -56.9 = -56.9
-1351.9x + x2 = -56.9

The x term is -1351.9x.  Take half its coefficient (-675.95).
Square it (456908.4025) and add it to both sides.

Add '456908.4025' to each side of the equation.
-1351.9x + 456908.4025 + x2 = -56.9 + 456908.4025

Reorder the terms:
456908.4025 + -1351.9x + x2 = -56.9 + 456908.4025

Combine like terms: -56.9 + 456908.4025 = 456851.5025
456908.4025 + -1351.9x + x2 = 456851.5025

Factor a perfect square on the left side:
(x + -675.95)(x + -675.95) = 456851.5025

Calculate the square root of the right side: 675.907909778

Break this problem into two subproblems by setting 
(x + -675.95) equal to 675.907909778 and -675.907909778.


Subproblem 1
x + -675.95 = 675.907909778

Simplifying
x + -675.95 = 675.907909778

Reorder the terms:
-675.95 + x = 675.907909778

Solving
-675.95 + x = 675.907909778

Solving for variable 'x'.

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

Add '675.95' to each side of the equation.
-675.95 + 675.95 + x = 675.907909778 + 675.95

Combine like terms: -675.95 + 675.95 = 0.00
0.00 + x = 675.907909778 + 675.95
x = 675.907909778 + 675.95

Combine like terms: 675.907909778 + 675.95 = 1351.857909778
x = 1351.857909778

Simplifying
x = 1351.857909778


Subproblem 2
x + -675.95 = -675.907909778

Simplifying
x + -675.95 = -675.907909778

Reorder the terms:
-675.95 + x = -675.907909778

Solving
-675.95 + x = -675.907909778

Solving for variable 'x'.

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

Add '675.95' to each side of the equation.
-675.95 + 675.95 + x = -675.907909778 + 675.95

Combine like terms: -675.95 + 675.95 = 0.00
0.00 + x = -675.907909778 + 675.95
x = -675.907909778 + 675.95

Combine like terms: -675.907909778 + 675.95 = 0.042090222
x = 0.042090222

Simplifying
x = 0.042090222


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1351.857909778, 0.042090222}

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