260=x^2+8x

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Solution for 260=x^2+8x equation:


Simplifying
260 = x2 + 8x

Reorder the terms:
260 = 8x + x2

Solving
260 = 8x + x2

Solving for variable 'x'.

Reorder the terms:
260 + -8x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
260 + -8x + -1x2 = 0 + x2 + -1x2
260 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
260 + -8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-260 + 8x + x2 = 0

Move the constant term to the right:

Add '260' to each side of the equation.
-260 + 8x + 260 + x2 = 0 + 260

Reorder the terms:
-260 + 260 + 8x + x2 = 0 + 260

Combine like terms: -260 + 260 = 0
0 + 8x + x2 = 0 + 260
8x + x2 = 0 + 260

Combine like terms: 0 + 260 = 260
8x + x2 = 260

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 = 260 + 16

Reorder the terms:
16 + 8x + x2 = 260 + 16

Combine like terms: 260 + 16 = 276
16 + 8x + x2 = 276

Factor a perfect square on the left side:
(x + 4)(x + 4) = 276

Calculate the square root of the right side: 16.613247726

Break this problem into two subproblems by setting 
(x + 4) equal to 16.613247726 and -16.613247726.

Subproblem 1

x + 4 = 16.613247726 Simplifying x + 4 = 16.613247726 Reorder the terms: 4 + x = 16.613247726 Solving 4 + x = 16.613247726 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 = 16.613247726 + -4 Combine like terms: 4 + -4 = 0 0 + x = 16.613247726 + -4 x = 16.613247726 + -4 Combine like terms: 16.613247726 + -4 = 12.613247726 x = 12.613247726 Simplifying x = 12.613247726

Subproblem 2

x + 4 = -16.613247726 Simplifying x + 4 = -16.613247726 Reorder the terms: 4 + x = -16.613247726 Solving 4 + x = -16.613247726 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 = -16.613247726 + -4 Combine like terms: 4 + -4 = 0 0 + x = -16.613247726 + -4 x = -16.613247726 + -4 Combine like terms: -16.613247726 + -4 = -20.613247726 x = -20.613247726 Simplifying x = -20.613247726

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.613247726, -20.613247726}

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