x^2+8x-196=0

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Solution for x^2+8x-196=0 equation:


Simplifying
x2 + 8x + -196 = 0

Reorder the terms:
-196 + 8x + x2 = 0

Solving
-196 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '196' to each side of the equation.
-196 + 8x + 196 + x2 = 0 + 196

Reorder the terms:
-196 + 196 + 8x + x2 = 0 + 196

Combine like terms: -196 + 196 = 0
0 + 8x + x2 = 0 + 196
8x + x2 = 0 + 196

Combine like terms: 0 + 196 = 196
8x + x2 = 196

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 = 196 + 16

Reorder the terms:
16 + 8x + x2 = 196 + 16

Combine like terms: 196 + 16 = 212
16 + 8x + x2 = 212

Factor a perfect square on the left side:
(x + 4)(x + 4) = 212

Calculate the square root of the right side: 14.560219779

Break this problem into two subproblems by setting 
(x + 4) equal to 14.560219779 and -14.560219779.

Subproblem 1

x + 4 = 14.560219779 Simplifying x + 4 = 14.560219779 Reorder the terms: 4 + x = 14.560219779 Solving 4 + x = 14.560219779 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 = 14.560219779 + -4 Combine like terms: 4 + -4 = 0 0 + x = 14.560219779 + -4 x = 14.560219779 + -4 Combine like terms: 14.560219779 + -4 = 10.560219779 x = 10.560219779 Simplifying x = 10.560219779

Subproblem 2

x + 4 = -14.560219779 Simplifying x + 4 = -14.560219779 Reorder the terms: 4 + x = -14.560219779 Solving 4 + x = -14.560219779 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 = -14.560219779 + -4 Combine like terms: 4 + -4 = 0 0 + x = -14.560219779 + -4 x = -14.560219779 + -4 Combine like terms: -14.560219779 + -4 = -18.560219779 x = -18.560219779 Simplifying x = -18.560219779

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.560219779, -18.560219779}

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