x^2+14x+46=0

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Solution for x^2+14x+46=0 equation:


Simplifying
x2 + 14x + 46 = 0

Reorder the terms:
46 + 14x + x2 = 0

Solving
46 + 14x + 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 + 14x + -46 + x2 = 0 + -46

Reorder the terms:
46 + -46 + 14x + x2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + 14x + x2 = 0 + -46
14x + x2 = 0 + -46

Combine like terms: 0 + -46 = -46
14x + x2 = -46

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -46 + 49

Reorder the terms:
49 + 14x + x2 = -46 + 49

Combine like terms: -46 + 49 = 3
49 + 14x + x2 = 3

Factor a perfect square on the left side:
(x + 7)(x + 7) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 7) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + 7 = 1.732050808 Simplifying x + 7 = 1.732050808 Reorder the terms: 7 + x = 1.732050808 Solving 7 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 1.732050808 + -7 Combine like terms: 7 + -7 = 0 0 + x = 1.732050808 + -7 x = 1.732050808 + -7 Combine like terms: 1.732050808 + -7 = -5.267949192 x = -5.267949192 Simplifying x = -5.267949192

Subproblem 2

x + 7 = -1.732050808 Simplifying x + 7 = -1.732050808 Reorder the terms: 7 + x = -1.732050808 Solving 7 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -1.732050808 + -7 Combine like terms: 7 + -7 = 0 0 + x = -1.732050808 + -7 x = -1.732050808 + -7 Combine like terms: -1.732050808 + -7 = -8.732050808 x = -8.732050808 Simplifying x = -8.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.267949192, -8.732050808}

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