x^2+14x-47=6

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Solution for x^2+14x-47=6 equation:


Simplifying
x2 + 14x + -47 = 6

Reorder the terms:
-47 + 14x + x2 = 6

Solving
-47 + 14x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-47 + -6 + 14x + x2 = 6 + -6

Combine like terms: -47 + -6 = -53
-53 + 14x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-53 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '53' to each side of the equation.
-53 + 14x + 53 + x2 = 0 + 53

Reorder the terms:
-53 + 53 + 14x + x2 = 0 + 53

Combine like terms: -53 + 53 = 0
0 + 14x + x2 = 0 + 53
14x + x2 = 0 + 53

Combine like terms: 0 + 53 = 53
14x + x2 = 53

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 = 53 + 49

Reorder the terms:
49 + 14x + x2 = 53 + 49

Combine like terms: 53 + 49 = 102
49 + 14x + x2 = 102

Factor a perfect square on the left side:
(x + 7)(x + 7) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(x + 7) equal to 10.099504938 and -10.099504938.

Subproblem 1

x + 7 = 10.099504938 Simplifying x + 7 = 10.099504938 Reorder the terms: 7 + x = 10.099504938 Solving 7 + x = 10.099504938 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 = 10.099504938 + -7 Combine like terms: 7 + -7 = 0 0 + x = 10.099504938 + -7 x = 10.099504938 + -7 Combine like terms: 10.099504938 + -7 = 3.099504938 x = 3.099504938 Simplifying x = 3.099504938

Subproblem 2

x + 7 = -10.099504938 Simplifying x + 7 = -10.099504938 Reorder the terms: 7 + x = -10.099504938 Solving 7 + x = -10.099504938 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 = -10.099504938 + -7 Combine like terms: 7 + -7 = 0 0 + x = -10.099504938 + -7 x = -10.099504938 + -7 Combine like terms: -10.099504938 + -7 = -17.099504938 x = -17.099504938 Simplifying x = -17.099504938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.099504938, -17.099504938}

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