4x^2+20x-25=0

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Solution for 4x^2+20x-25=0 equation:


Simplifying
4x2 + 20x + -25 = 0

Reorder the terms:
-25 + 20x + 4x2 = 0

Solving
-25 + 20x + 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'.
-6.25 + 5x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 5x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 5x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 5x + x2 = 0 + 6.25
5x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
5x + x2 = 6.25

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 = 6.25 + 6.25

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

Combine like terms: 6.25 + 6.25 = 12.5
6.25 + 5x + x2 = 12.5

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 12.5

Calculate the square root of the right side: 3.535533906

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.535533906 and -3.535533906.

Subproblem 1

x + 2.5 = 3.535533906 Simplifying x + 2.5 = 3.535533906 Reorder the terms: 2.5 + x = 3.535533906 Solving 2.5 + x = 3.535533906 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 = 3.535533906 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.535533906 + -2.5 x = 3.535533906 + -2.5 Combine like terms: 3.535533906 + -2.5 = 1.035533906 x = 1.035533906 Simplifying x = 1.035533906

Subproblem 2

x + 2.5 = -3.535533906 Simplifying x + 2.5 = -3.535533906 Reorder the terms: 2.5 + x = -3.535533906 Solving 2.5 + x = -3.535533906 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 = -3.535533906 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.535533906 + -2.5 x = -3.535533906 + -2.5 Combine like terms: -3.535533906 + -2.5 = -6.035533906 x = -6.035533906 Simplifying x = -6.035533906

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.035533906, -6.035533906}

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