4x^2-125x+95=0

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Solution for 4x^2-125x+95=0 equation:


Simplifying
4x2 + -125x + 95 = 0

Reorder the terms:
95 + -125x + 4x2 = 0

Solving
95 + -125x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
23.75 + -31.25x + x2 = 0

Move the constant term to the right:

Add '-23.75' to each side of the equation.
23.75 + -31.25x + -23.75 + x2 = 0 + -23.75

Reorder the terms:
23.75 + -23.75 + -31.25x + x2 = 0 + -23.75

Combine like terms: 23.75 + -23.75 = 0.00
0.00 + -31.25x + x2 = 0 + -23.75
-31.25x + x2 = 0 + -23.75

Combine like terms: 0 + -23.75 = -23.75
-31.25x + x2 = -23.75

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 = -23.75 + 244.140625

Reorder the terms:
244.140625 + -31.25x + x2 = -23.75 + 244.140625

Combine like terms: -23.75 + 244.140625 = 220.390625
244.140625 + -31.25x + x2 = 220.390625

Factor a perfect square on the left side:
(x + -15.625)(x + -15.625) = 220.390625

Calculate the square root of the right side: 14.8455591

Break this problem into two subproblems by setting 
(x + -15.625) equal to 14.8455591 and -14.8455591.

Subproblem 1

x + -15.625 = 14.8455591 Simplifying x + -15.625 = 14.8455591 Reorder the terms: -15.625 + x = 14.8455591 Solving -15.625 + x = 14.8455591 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 = 14.8455591 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + x = 14.8455591 + 15.625 x = 14.8455591 + 15.625 Combine like terms: 14.8455591 + 15.625 = 30.4705591 x = 30.4705591 Simplifying x = 30.4705591

Subproblem 2

x + -15.625 = -14.8455591 Simplifying x + -15.625 = -14.8455591 Reorder the terms: -15.625 + x = -14.8455591 Solving -15.625 + x = -14.8455591 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 = -14.8455591 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + x = -14.8455591 + 15.625 x = -14.8455591 + 15.625 Combine like terms: -14.8455591 + 15.625 = 0.7794409 x = 0.7794409 Simplifying x = 0.7794409

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30.4705591, 0.7794409}

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