2x^2+45x+125=0

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Solution for 2x^2+45x+125=0 equation:


Simplifying
2x2 + 45x + 125 = 0

Reorder the terms:
125 + 45x + 2x2 = 0

Solving
125 + 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'.
62.5 + 22.5x + x2 = 0

Move the constant term to the right:

Add '-62.5' to each side of the equation.
62.5 + 22.5x + -62.5 + x2 = 0 + -62.5

Reorder the terms:
62.5 + -62.5 + 22.5x + x2 = 0 + -62.5

Combine like terms: 62.5 + -62.5 = 0.0
0.0 + 22.5x + x2 = 0 + -62.5
22.5x + x2 = 0 + -62.5

Combine like terms: 0 + -62.5 = -62.5
22.5x + x2 = -62.5

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 = -62.5 + 126.5625

Reorder the terms:
126.5625 + 22.5x + x2 = -62.5 + 126.5625

Combine like terms: -62.5 + 126.5625 = 64.0625
126.5625 + 22.5x + x2 = 64.0625

Factor a perfect square on the left side:
(x + 11.25)(x + 11.25) = 64.0625

Calculate the square root of the right side: 8.003905297

Break this problem into two subproblems by setting 
(x + 11.25) equal to 8.003905297 and -8.003905297.

Subproblem 1

x + 11.25 = 8.003905297 Simplifying x + 11.25 = 8.003905297 Reorder the terms: 11.25 + x = 8.003905297 Solving 11.25 + x = 8.003905297 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 = 8.003905297 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 8.003905297 + -11.25 x = 8.003905297 + -11.25 Combine like terms: 8.003905297 + -11.25 = -3.246094703 x = -3.246094703 Simplifying x = -3.246094703

Subproblem 2

x + 11.25 = -8.003905297 Simplifying x + 11.25 = -8.003905297 Reorder the terms: 11.25 + x = -8.003905297 Solving 11.25 + x = -8.003905297 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 = -8.003905297 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -8.003905297 + -11.25 x = -8.003905297 + -11.25 Combine like terms: -8.003905297 + -11.25 = -19.253905297 x = -19.253905297 Simplifying x = -19.253905297

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.246094703, -19.253905297}

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