x^2+8x-98=-6

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Solution for x^2+8x-98=-6 equation:


Simplifying
x2 + 8x + -98 = -6

Reorder the terms:
-98 + 8x + x2 = -6

Solving
-98 + 8x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
-98 + 6 + 8x + x2 = -6 + 6

Combine like terms: -98 + 6 = -92
-92 + 8x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
-92 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '92' to each side of the equation.
-92 + 8x + 92 + x2 = 0 + 92

Reorder the terms:
-92 + 92 + 8x + x2 = 0 + 92

Combine like terms: -92 + 92 = 0
0 + 8x + x2 = 0 + 92
8x + x2 = 0 + 92

Combine like terms: 0 + 92 = 92
8x + x2 = 92

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 92 + 16

Reorder the terms:
16 + 8x + x2 = 92 + 16

Combine like terms: 92 + 16 = 108
16 + 8x + x2 = 108

Factor a perfect square on the left side:
(x + 4)(x + 4) = 108

Calculate the square root of the right side: 10.392304845

Break this problem into two subproblems by setting 
(x + 4) equal to 10.392304845 and -10.392304845.

Subproblem 1

x + 4 = 10.392304845 Simplifying x + 4 = 10.392304845 Reorder the terms: 4 + x = 10.392304845 Solving 4 + x = 10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 10.392304845 + -4 Combine like terms: 4 + -4 = 0 0 + x = 10.392304845 + -4 x = 10.392304845 + -4 Combine like terms: 10.392304845 + -4 = 6.392304845 x = 6.392304845 Simplifying x = 6.392304845

Subproblem 2

x + 4 = -10.392304845 Simplifying x + 4 = -10.392304845 Reorder the terms: 4 + x = -10.392304845 Solving 4 + x = -10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -10.392304845 + -4 Combine like terms: 4 + -4 = 0 0 + x = -10.392304845 + -4 x = -10.392304845 + -4 Combine like terms: -10.392304845 + -4 = -14.392304845 x = -14.392304845 Simplifying x = -14.392304845

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.392304845, -14.392304845}

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