x^2+5x-915=0

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Solution for x^2+5x-915=0 equation:


Simplifying
x2 + 5x + -915 = 0

Reorder the terms:
-915 + 5x + x2 = 0

Solving
-915 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '915' to each side of the equation.
-915 + 5x + 915 + x2 = 0 + 915

Reorder the terms:
-915 + 915 + 5x + x2 = 0 + 915

Combine like terms: -915 + 915 = 0
0 + 5x + x2 = 0 + 915
5x + x2 = 0 + 915

Combine like terms: 0 + 915 = 915
5x + x2 = 915

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 = 915 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 915 + 6.25

Combine like terms: 915 + 6.25 = 921.25
6.25 + 5x + x2 = 921.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 921.25

Calculate the square root of the right side: 30.352100422

Break this problem into two subproblems by setting 
(x + 2.5) equal to 30.352100422 and -30.352100422.

Subproblem 1

x + 2.5 = 30.352100422 Simplifying x + 2.5 = 30.352100422 Reorder the terms: 2.5 + x = 30.352100422 Solving 2.5 + x = 30.352100422 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 = 30.352100422 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 30.352100422 + -2.5 x = 30.352100422 + -2.5 Combine like terms: 30.352100422 + -2.5 = 27.852100422 x = 27.852100422 Simplifying x = 27.852100422

Subproblem 2

x + 2.5 = -30.352100422 Simplifying x + 2.5 = -30.352100422 Reorder the terms: 2.5 + x = -30.352100422 Solving 2.5 + x = -30.352100422 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 = -30.352100422 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -30.352100422 + -2.5 x = -30.352100422 + -2.5 Combine like terms: -30.352100422 + -2.5 = -32.852100422 x = -32.852100422 Simplifying x = -32.852100422

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.852100422, -32.852100422}

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