x^2-625x+7056=0

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Solution for x^2-625x+7056=0 equation:


Simplifying
x2 + -625x + 7056 = 0

Reorder the terms:
7056 + -625x + x2 = 0

Solving
7056 + -625x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7056' to each side of the equation.
7056 + -625x + -7056 + x2 = 0 + -7056

Reorder the terms:
7056 + -7056 + -625x + x2 = 0 + -7056

Combine like terms: 7056 + -7056 = 0
0 + -625x + x2 = 0 + -7056
-625x + x2 = 0 + -7056

Combine like terms: 0 + -7056 = -7056
-625x + x2 = -7056

The x term is -625x.  Take half its coefficient (-312.5).
Square it (97656.25) and add it to both sides.

Add '97656.25' to each side of the equation.
-625x + 97656.25 + x2 = -7056 + 97656.25

Reorder the terms:
97656.25 + -625x + x2 = -7056 + 97656.25

Combine like terms: -7056 + 97656.25 = 90600.25
97656.25 + -625x + x2 = 90600.25

Factor a perfect square on the left side:
(x + -312.5)(x + -312.5) = 90600.25

Calculate the square root of the right side: 300.99875415

Break this problem into two subproblems by setting 
(x + -312.5) equal to 300.99875415 and -300.99875415.

Subproblem 1

x + -312.5 = 300.99875415 Simplifying x + -312.5 = 300.99875415 Reorder the terms: -312.5 + x = 300.99875415 Solving -312.5 + x = 300.99875415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '312.5' to each side of the equation. -312.5 + 312.5 + x = 300.99875415 + 312.5 Combine like terms: -312.5 + 312.5 = 0.0 0.0 + x = 300.99875415 + 312.5 x = 300.99875415 + 312.5 Combine like terms: 300.99875415 + 312.5 = 613.49875415 x = 613.49875415 Simplifying x = 613.49875415

Subproblem 2

x + -312.5 = -300.99875415 Simplifying x + -312.5 = -300.99875415 Reorder the terms: -312.5 + x = -300.99875415 Solving -312.5 + x = -300.99875415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '312.5' to each side of the equation. -312.5 + 312.5 + x = -300.99875415 + 312.5 Combine like terms: -312.5 + 312.5 = 0.0 0.0 + x = -300.99875415 + 312.5 x = -300.99875415 + 312.5 Combine like terms: -300.99875415 + 312.5 = 11.50124585 x = 11.50124585 Simplifying x = 11.50124585

Solution

The solution to the problem is based on the solutions from the subproblems. x = {613.49875415, 11.50124585}

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