2x^2+10x=-5

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Solution for 2x^2+10x=-5 equation:


Simplifying
2x2 + 10x = -5

Reorder the terms:
10x + 2x2 = -5

Solving
10x + 2x2 = -5

Solving for variable 'x'.

Reorder the terms:
5 + 10x + 2x2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 10x + 2x2 = 0

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

Divide each side by '2'.
2.5 + 5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 5x + x2 = 0 + -2.5
5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
5x + x2 = -2.5

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 = -2.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -2.5 + 6.25

Combine like terms: -2.5 + 6.25 = 3.75
6.25 + 5x + x2 = 3.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.936491673 and -1.936491673.

Subproblem 1

x + 2.5 = 1.936491673 Simplifying x + 2.5 = 1.936491673 Reorder the terms: 2.5 + x = 1.936491673 Solving 2.5 + x = 1.936491673 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 = 1.936491673 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.936491673 + -2.5 x = 1.936491673 + -2.5 Combine like terms: 1.936491673 + -2.5 = -0.563508327 x = -0.563508327 Simplifying x = -0.563508327

Subproblem 2

x + 2.5 = -1.936491673 Simplifying x + 2.5 = -1.936491673 Reorder the terms: 2.5 + x = -1.936491673 Solving 2.5 + x = -1.936491673 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 = -1.936491673 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.936491673 + -2.5 x = -1.936491673 + -2.5 Combine like terms: -1.936491673 + -2.5 = -4.436491673 x = -4.436491673 Simplifying x = -4.436491673

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.563508327, -4.436491673}

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