1.25x^2-40x+160=0

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Solution for 1.25x^2-40x+160=0 equation:


Simplifying
1.25x2 + -40x + 160 = 0

Reorder the terms:
160 + -40x + 1.25x2 = 0

Solving
160 + -40x + 1.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.25'.
128 + -32x + x2 = 0

Move the constant term to the right:

Add '-128' to each side of the equation.
128 + -32x + -128 + x2 = 0 + -128

Reorder the terms:
128 + -128 + -32x + x2 = 0 + -128

Combine like terms: 128 + -128 = 0
0 + -32x + x2 = 0 + -128
-32x + x2 = 0 + -128

Combine like terms: 0 + -128 = -128
-32x + x2 = -128

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = -128 + 256

Reorder the terms:
256 + -32x + x2 = -128 + 256

Combine like terms: -128 + 256 = 128
256 + -32x + x2 = 128

Factor a perfect square on the left side:
(x + -16)(x + -16) = 128

Calculate the square root of the right side: 11.313708499

Break this problem into two subproblems by setting 
(x + -16) equal to 11.313708499 and -11.313708499.

Subproblem 1

x + -16 = 11.313708499 Simplifying x + -16 = 11.313708499 Reorder the terms: -16 + x = 11.313708499 Solving -16 + x = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 11.313708499 + 16 Combine like terms: -16 + 16 = 0 0 + x = 11.313708499 + 16 x = 11.313708499 + 16 Combine like terms: 11.313708499 + 16 = 27.313708499 x = 27.313708499 Simplifying x = 27.313708499

Subproblem 2

x + -16 = -11.313708499 Simplifying x + -16 = -11.313708499 Reorder the terms: -16 + x = -11.313708499 Solving -16 + x = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -11.313708499 + 16 Combine like terms: -16 + 16 = 0 0 + x = -11.313708499 + 16 x = -11.313708499 + 16 Combine like terms: -11.313708499 + 16 = 4.686291501 x = 4.686291501 Simplifying x = 4.686291501

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.313708499, 4.686291501}

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