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 = 10.25
56.25 + 15x + x2 = 10.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 7.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + 7.5 = 3.201562119 Simplifying x + 7.5 = 3.201562119 Reorder the terms: 7.5 + x = 3.201562119 Solving 7.5 + x = 3.201562119 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 = 3.201562119 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 3.201562119 + -7.5 x = 3.201562119 + -7.5 Combine like terms: 3.201562119 + -7.5 = -4.298437881 x = -4.298437881 Simplifying x = -4.298437881

Subproblem 2

x + 7.5 = -3.201562119 Simplifying x + 7.5 = -3.201562119 Reorder the terms: 7.5 + x = -3.201562119 Solving 7.5 + x = -3.201562119 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 = -3.201562119 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -3.201562119 + -7.5 x = -3.201562119 + -7.5 Combine like terms: -3.201562119 + -7.5 = -10.701562119 x = -10.701562119 Simplifying x = -10.701562119

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.298437881, -10.701562119}

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