x^2+8x-69=0

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Solution for x^2+8x-69=0 equation:


Simplifying
x2 + 8x + -69 = 0

Reorder the terms:
-69 + 8x + x2 = 0

Solving
-69 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '69' to each side of the equation.
-69 + 8x + 69 + x2 = 0 + 69

Reorder the terms:
-69 + 69 + 8x + x2 = 0 + 69

Combine like terms: -69 + 69 = 0
0 + 8x + x2 = 0 + 69
8x + x2 = 0 + 69

Combine like terms: 0 + 69 = 69
8x + x2 = 69

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 = 69 + 16

Reorder the terms:
16 + 8x + x2 = 69 + 16

Combine like terms: 69 + 16 = 85
16 + 8x + x2 = 85

Factor a perfect square on the left side:
(x + 4)(x + 4) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(x + 4) equal to 9.219544457 and -9.219544457.

Subproblem 1

x + 4 = 9.219544457 Simplifying x + 4 = 9.219544457 Reorder the terms: 4 + x = 9.219544457 Solving 4 + x = 9.219544457 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 = 9.219544457 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.219544457 + -4 x = 9.219544457 + -4 Combine like terms: 9.219544457 + -4 = 5.219544457 x = 5.219544457 Simplifying x = 5.219544457

Subproblem 2

x + 4 = -9.219544457 Simplifying x + 4 = -9.219544457 Reorder the terms: 4 + x = -9.219544457 Solving 4 + x = -9.219544457 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 = -9.219544457 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.219544457 + -4 x = -9.219544457 + -4 Combine like terms: -9.219544457 + -4 = -13.219544457 x = -13.219544457 Simplifying x = -13.219544457

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.219544457, -13.219544457}

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