x^2+15x-46=0

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Solution for x^2+15x-46=0 equation: 


Simplifying
x2 + 15x + -46 = 0

Reorder the terms:
-46 + 15x + x2 = 0

Solving
-46 + 15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 15x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + 15x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 15x + x2 = 0 + 46
15x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
15x + x2 = 46

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 = 46 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 46 + 56.25

Combine like terms: 46 + 56.25 = 102.25
56.25 + 15x + x2 = 102.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(x + 7.5) equal to 10.111874208 and -10.111874208.


Subproblem 1
x + 7.5 = 10.111874208

Simplifying
x + 7.5 = 10.111874208

Reorder the terms:
7.5 + x = 10.111874208

Solving
7.5 + x = 10.111874208

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 = 10.111874208 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 10.111874208 + -7.5
x = 10.111874208 + -7.5

Combine like terms: 10.111874208 + -7.5 = 2.611874208
x = 2.611874208

Simplifying
x = 2.611874208


Subproblem 2
x + 7.5 = -10.111874208

Simplifying
x + 7.5 = -10.111874208

Reorder the terms:
7.5 + x = -10.111874208

Solving
7.5 + x = -10.111874208

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 = -10.111874208 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -10.111874208 + -7.5
x = -10.111874208 + -7.5

Combine like terms: -10.111874208 + -7.5 = -17.611874208
x = -17.611874208

Simplifying
x = -17.611874208


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.611874208, -17.611874208}

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