x^2+14x+43=7

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Solution for x^2+14x+43=7 equation:


Simplifying
x2 + 14x + 43 = 7

Reorder the terms:
43 + 14x + x2 = 7

Solving
43 + 14x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
43 + -7 + 14x + x2 = 7 + -7

Combine like terms: 43 + -7 = 36
36 + 14x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
36 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 14x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + 14x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 14x + x2 = 0 + -36
14x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
14x + x2 = -36

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 = -36 + 49

Reorder the terms:
49 + 14x + x2 = -36 + 49

Combine like terms: -36 + 49 = 13
49 + 14x + x2 = 13

Factor a perfect square on the left side:
(x + 7)(x + 7) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 7) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + 7 = 3.605551275 Simplifying x + 7 = 3.605551275 Reorder the terms: 7 + x = 3.605551275 Solving 7 + x = 3.605551275 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 = 3.605551275 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.605551275 + -7 x = 3.605551275 + -7 Combine like terms: 3.605551275 + -7 = -3.394448725 x = -3.394448725 Simplifying x = -3.394448725

Subproblem 2

x + 7 = -3.605551275 Simplifying x + 7 = -3.605551275 Reorder the terms: 7 + x = -3.605551275 Solving 7 + x = -3.605551275 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 = -3.605551275 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.605551275 + -7 x = -3.605551275 + -7 Combine like terms: -3.605551275 + -7 = -10.605551275 x = -10.605551275 Simplifying x = -10.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.394448725, -10.605551275}

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