x^2+15x=-4

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Solution for x^2+15x=-4 equation:


Simplifying
x2 + 15x = -4

Reorder the terms:
15x + x2 = -4

Solving
15x + x2 = -4

Solving for variable 'x'.

Reorder the terms:
4 + 15x + x2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 15x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 15x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 15x + x2 = 0 + -4
15x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
15x + x2 = -4

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -4 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -4 + 56.25

Combine like terms: -4 + 56.25 = 52.25
56.25 + 15x + x2 = 52.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(x + 7.5) equal to 7.228416147 and -7.228416147.

Subproblem 1

x + 7.5 = 7.228416147 Simplifying x + 7.5 = 7.228416147 Reorder the terms: 7.5 + x = 7.228416147 Solving 7.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 7.228416147 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.228416147 + -7.5 x = 7.228416147 + -7.5 Combine like terms: 7.228416147 + -7.5 = -0.271583853 x = -0.271583853 Simplifying x = -0.271583853

Subproblem 2

x + 7.5 = -7.228416147 Simplifying x + 7.5 = -7.228416147 Reorder the terms: 7.5 + x = -7.228416147 Solving 7.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -7.228416147 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.228416147 + -7.5 x = -7.228416147 + -7.5 Combine like terms: -7.228416147 + -7.5 = -14.728416147 x = -14.728416147 Simplifying x = -14.728416147

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.271583853, -14.728416147}

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