2x^2-25x-10=0

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Solution for 2x^2-25x-10=0 equation:


Simplifying
2x2 + -25x + -10 = 0

Reorder the terms:
-10 + -25x + 2x2 = 0

Solving
-10 + -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'.
-5 + -12.5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -12.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -12.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -12.5x + x2 = 0 + 5
-12.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-12.5x + x2 = 5

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 = 5 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = 5 + 39.0625

Combine like terms: 5 + 39.0625 = 44.0625
39.0625 + -12.5x + x2 = 44.0625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 44.0625

Calculate the square root of the right side: 6.637959024

Break this problem into two subproblems by setting 
(x + -6.25) equal to 6.637959024 and -6.637959024.

Subproblem 1

x + -6.25 = 6.637959024 Simplifying x + -6.25 = 6.637959024 Reorder the terms: -6.25 + x = 6.637959024 Solving -6.25 + x = 6.637959024 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 = 6.637959024 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 6.637959024 + 6.25 x = 6.637959024 + 6.25 Combine like terms: 6.637959024 + 6.25 = 12.887959024 x = 12.887959024 Simplifying x = 12.887959024

Subproblem 2

x + -6.25 = -6.637959024 Simplifying x + -6.25 = -6.637959024 Reorder the terms: -6.25 + x = -6.637959024 Solving -6.25 + x = -6.637959024 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 = -6.637959024 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -6.637959024 + 6.25 x = -6.637959024 + 6.25 Combine like terms: -6.637959024 + 6.25 = -0.387959024 x = -0.387959024 Simplifying x = -0.387959024

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.887959024, -0.387959024}

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