4x^2-125x=-25

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Solution for 4x^2-125x=-25 equation:


Simplifying
4x2 + -125x = -25

Reorder the terms:
-125x + 4x2 = -25

Solving
-125x + 4x2 = -25

Solving for variable 'x'.

Reorder the terms:
25 + -125x + 4x2 = -25 + 25

Combine like terms: -25 + 25 = 0
25 + -125x + 4x2 = 0

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

Divide each side by '4'.
6.25 + -31.25x + x2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + -31.25x + -6.25 + x2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + -31.25x + x2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + -31.25x + x2 = 0 + -6.25
-31.25x + x2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
-31.25x + x2 = -6.25

The x term is -31.25x.  Take half its coefficient (-15.625).
Square it (244.140625) and add it to both sides.

Add '244.140625' to each side of the equation.
-31.25x + 244.140625 + x2 = -6.25 + 244.140625

Reorder the terms:
244.140625 + -31.25x + x2 = -6.25 + 244.140625

Combine like terms: -6.25 + 244.140625 = 237.890625
244.140625 + -31.25x + x2 = 237.890625

Factor a perfect square on the left side:
(x + -15.625)(x + -15.625) = 237.890625

Calculate the square root of the right side: 15.423703349

Break this problem into two subproblems by setting 
(x + -15.625) equal to 15.423703349 and -15.423703349.

Subproblem 1

x + -15.625 = 15.423703349 Simplifying x + -15.625 = 15.423703349 Reorder the terms: -15.625 + x = 15.423703349 Solving -15.625 + x = 15.423703349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + x = 15.423703349 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + x = 15.423703349 + 15.625 x = 15.423703349 + 15.625 Combine like terms: 15.423703349 + 15.625 = 31.048703349 x = 31.048703349 Simplifying x = 31.048703349

Subproblem 2

x + -15.625 = -15.423703349 Simplifying x + -15.625 = -15.423703349 Reorder the terms: -15.625 + x = -15.423703349 Solving -15.625 + x = -15.423703349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + x = -15.423703349 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + x = -15.423703349 + 15.625 x = -15.423703349 + 15.625 Combine like terms: -15.423703349 + 15.625 = 0.201296651 x = 0.201296651 Simplifying x = 0.201296651

Solution

The solution to the problem is based on the solutions from the subproblems. x = {31.048703349, 0.201296651}

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