2x^2-45x-25=0

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Solution for 2x^2-45x-25=0 equation:


Simplifying
2x2 + -45x + -25 = 0

Reorder the terms:
-25 + -45x + 2x2 = 0

Solving
-25 + -45x + 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'.
-12.5 + -22.5x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -22.5x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -22.5x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -22.5x + x2 = 0 + 12.5
-22.5x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-22.5x + x2 = 12.5

The x term is -22.5x.  Take half its coefficient (-11.25).
Square it (126.5625) and add it to both sides.

Add '126.5625' to each side of the equation.
-22.5x + 126.5625 + x2 = 12.5 + 126.5625

Reorder the terms:
126.5625 + -22.5x + x2 = 12.5 + 126.5625

Combine like terms: 12.5 + 126.5625 = 139.0625
126.5625 + -22.5x + x2 = 139.0625

Factor a perfect square on the left side:
(x + -11.25)(x + -11.25) = 139.0625

Calculate the square root of the right side: 11.792476415

Break this problem into two subproblems by setting 
(x + -11.25) equal to 11.792476415 and -11.792476415.

Subproblem 1

x + -11.25 = 11.792476415 Simplifying x + -11.25 = 11.792476415 Reorder the terms: -11.25 + x = 11.792476415 Solving -11.25 + x = 11.792476415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 11.792476415 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 11.792476415 + 11.25 x = 11.792476415 + 11.25 Combine like terms: 11.792476415 + 11.25 = 23.042476415 x = 23.042476415 Simplifying x = 23.042476415

Subproblem 2

x + -11.25 = -11.792476415 Simplifying x + -11.25 = -11.792476415 Reorder the terms: -11.25 + x = -11.792476415 Solving -11.25 + x = -11.792476415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -11.792476415 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -11.792476415 + 11.25 x = -11.792476415 + 11.25 Combine like terms: -11.792476415 + 11.25 = -0.542476415 x = -0.542476415 Simplifying x = -0.542476415

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.042476415, -0.542476415}

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