2x(-4x+20)=25

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Solution for 2x(-4x+20)=25 equation:


Simplifying
2x(-4x + 20) = 25

Reorder the terms:
2x(20 + -4x) = 25
(20 * 2x + -4x * 2x) = 25
(40x + -8x2) = 25

Solving
40x + -8x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 40x + -8x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 40x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
3.125 + -5x + x2 = 0

Move the constant term to the right:

Add '-3.125' to each side of the equation.
3.125 + -5x + -3.125 + x2 = 0 + -3.125

Reorder the terms:
3.125 + -3.125 + -5x + x2 = 0 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + -5x + x2 = 0 + -3.125
-5x + x2 = 0 + -3.125

Combine like terms: 0 + -3.125 = -3.125
-5x + x2 = -3.125

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -3.125 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3.125 + 6.25

Combine like terms: -3.125 + 6.25 = 3.125
6.25 + -5x + x2 = 3.125

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.125

Calculate the square root of the right side: 1.767766953

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.767766953 and -1.767766953.

Subproblem 1

x + -2.5 = 1.767766953 Simplifying x + -2.5 = 1.767766953 Reorder the terms: -2.5 + x = 1.767766953 Solving -2.5 + x = 1.767766953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.767766953 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.767766953 + 2.5 x = 1.767766953 + 2.5 Combine like terms: 1.767766953 + 2.5 = 4.267766953 x = 4.267766953 Simplifying x = 4.267766953

Subproblem 2

x + -2.5 = -1.767766953 Simplifying x + -2.5 = -1.767766953 Reorder the terms: -2.5 + x = -1.767766953 Solving -2.5 + x = -1.767766953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.767766953 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.767766953 + 2.5 x = -1.767766953 + 2.5 Combine like terms: -1.767766953 + 2.5 = 0.732233047 x = 0.732233047 Simplifying x = 0.732233047

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.267766953, 0.732233047}

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