2x^2+10x-15=0

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Solution for 2x^2+10x-15=0 equation:


Simplifying
2x2 + 10x + -15 = 0

Reorder the terms:
-15 + 10x + 2x2 = 0

Solving
-15 + 10x + 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'.
-7.5 + 5x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 5x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 5x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 5x + x2 = 0 + 7.5
5x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
5x + x2 = 7.5

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 = 7.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 7.5 + 6.25

Combine like terms: 7.5 + 6.25 = 13.75
6.25 + 5x + x2 = 13.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 13.75

Calculate the square root of the right side: 3.708099244

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.708099244 and -3.708099244.

Subproblem 1

x + 2.5 = 3.708099244 Simplifying x + 2.5 = 3.708099244 Reorder the terms: 2.5 + x = 3.708099244 Solving 2.5 + x = 3.708099244 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 = 3.708099244 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.708099244 + -2.5 x = 3.708099244 + -2.5 Combine like terms: 3.708099244 + -2.5 = 1.208099244 x = 1.208099244 Simplifying x = 1.208099244

Subproblem 2

x + 2.5 = -3.708099244 Simplifying x + 2.5 = -3.708099244 Reorder the terms: 2.5 + x = -3.708099244 Solving 2.5 + x = -3.708099244 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 = -3.708099244 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.708099244 + -2.5 x = -3.708099244 + -2.5 Combine like terms: -3.708099244 + -2.5 = -6.208099244 x = -6.208099244 Simplifying x = -6.208099244

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.208099244, -6.208099244}

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