2x^2+25x-20=0

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


Simplifying
2x2 + 25x + -20 = 0

Reorder the terms:
-20 + 25x + 2x2 = 0

Solving
-20 + 25x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-10 + 12.5x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 12.5x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 12.5x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 12.5x + x2 = 0 + 10
12.5x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
12.5x + x2 = 10

The x term is 12.5x.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5x + 39.0625 + x2 = 10 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = 10 + 39.0625

Combine like terms: 10 + 39.0625 = 49.0625
39.0625 + 12.5x + x2 = 49.0625

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 49.0625

Calculate the square root of the right side: 7.004462863

Break this problem into two subproblems by setting 
(x + 6.25) equal to 7.004462863 and -7.004462863.

Subproblem 1

x + 6.25 = 7.004462863 Simplifying x + 6.25 = 7.004462863 Reorder the terms: 6.25 + x = 7.004462863 Solving 6.25 + x = 7.004462863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 7.004462863 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 7.004462863 + -6.25 x = 7.004462863 + -6.25 Combine like terms: 7.004462863 + -6.25 = 0.754462863 x = 0.754462863 Simplifying x = 0.754462863

Subproblem 2

x + 6.25 = -7.004462863 Simplifying x + 6.25 = -7.004462863 Reorder the terms: 6.25 + x = -7.004462863 Solving 6.25 + x = -7.004462863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -7.004462863 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -7.004462863 + -6.25 x = -7.004462863 + -6.25 Combine like terms: -7.004462863 + -6.25 = -13.254462863 x = -13.254462863 Simplifying x = -13.254462863

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.754462863, -13.254462863}

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