0=x^2-78.125x-15625

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Solution for 0=x^2-78.125x-15625 equation:


Simplifying
0 = x2 + -78.125x + -15625

Reorder the terms:
0 = -15625 + -78.125x + x2

Solving
0 = -15625 + -78.125x + x2

Solving for variable 'x'.

Combine like terms: 0 + 15625 = 15625
15625 + 78.125x + -1x2 = -15625 + -78.125x + x2 + 15625 + 78.125x + -1x2

Reorder the terms:
15625 + 78.125x + -1x2 = -15625 + 15625 + -78.125x + 78.125x + x2 + -1x2

Combine like terms: -15625 + 15625 = 0
15625 + 78.125x + -1x2 = 0 + -78.125x + 78.125x + x2 + -1x2
15625 + 78.125x + -1x2 = -78.125x + 78.125x + x2 + -1x2

Combine like terms: -78.125x + 78.125x = 0.000
15625 + 78.125x + -1x2 = 0.000 + x2 + -1x2
15625 + 78.125x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15625 + 78.125x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-15625 + -78.125x + x2 = 0

Move the constant term to the right:

Add '15625' to each side of the equation.
-15625 + -78.125x + 15625 + x2 = 0 + 15625

Reorder the terms:
-15625 + 15625 + -78.125x + x2 = 0 + 15625

Combine like terms: -15625 + 15625 = 0
0 + -78.125x + x2 = 0 + 15625
-78.125x + x2 = 0 + 15625

Combine like terms: 0 + 15625 = 15625
-78.125x + x2 = 15625

The x term is -78.125x.  Take half its coefficient (-39.0625).
Square it (1525.878906) and add it to both sides.

Add '1525.878906' to each side of the equation.
-78.125x + 1525.878906 + x2 = 15625 + 1525.878906

Reorder the terms:
1525.878906 + -78.125x + x2 = 15625 + 1525.878906

Combine like terms: 15625 + 1525.878906 = 17150.878906
1525.878906 + -78.125x + x2 = 17150.878906

Factor a perfect square on the left side:
(x + -39.0625)(x + -39.0625) = 17150.878906

Calculate the square root of the right side: 130.961364173

Break this problem into two subproblems by setting 
(x + -39.0625) equal to 130.961364173 and -130.961364173.

Subproblem 1

x + -39.0625 = 130.961364173 Simplifying x + -39.0625 = 130.961364173 Reorder the terms: -39.0625 + x = 130.961364173 Solving -39.0625 + x = 130.961364173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39.0625' to each side of the equation. -39.0625 + 39.0625 + x = 130.961364173 + 39.0625 Combine like terms: -39.0625 + 39.0625 = 0.0000 0.0000 + x = 130.961364173 + 39.0625 x = 130.961364173 + 39.0625 Combine like terms: 130.961364173 + 39.0625 = 170.023864173 x = 170.023864173 Simplifying x = 170.023864173

Subproblem 2

x + -39.0625 = -130.961364173 Simplifying x + -39.0625 = -130.961364173 Reorder the terms: -39.0625 + x = -130.961364173 Solving -39.0625 + x = -130.961364173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39.0625' to each side of the equation. -39.0625 + 39.0625 + x = -130.961364173 + 39.0625 Combine like terms: -39.0625 + 39.0625 = 0.0000 0.0000 + x = -130.961364173 + 39.0625 x = -130.961364173 + 39.0625 Combine like terms: -130.961364173 + 39.0625 = -91.898864173 x = -91.898864173 Simplifying x = -91.898864173

Solution

The solution to the problem is based on the solutions from the subproblems. x = {170.023864173, -91.898864173}

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