x^2+2x-56=0

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Solution for x^2+2x-56=0 equation:


Simplifying
x2 + 2x + -56 = 0

Reorder the terms:
-56 + 2x + x2 = 0

Solving
-56 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + 2x + 56 + x2 = 0 + 56

Reorder the terms:
-56 + 56 + 2x + x2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + 2x + x2 = 0 + 56
2x + x2 = 0 + 56

Combine like terms: 0 + 56 = 56
2x + x2 = 56

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 56 + 1

Reorder the terms:
1 + 2x + x2 = 56 + 1

Combine like terms: 56 + 1 = 57
1 + 2x + x2 = 57

Factor a perfect square on the left side:
(x + 1)(x + 1) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + 1) equal to 7.549834435 and -7.549834435.

Subproblem 1

x + 1 = 7.549834435 Simplifying x + 1 = 7.549834435 Reorder the terms: 1 + x = 7.549834435 Solving 1 + x = 7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 7.549834435 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.549834435 + -1 x = 7.549834435 + -1 Combine like terms: 7.549834435 + -1 = 6.549834435 x = 6.549834435 Simplifying x = 6.549834435

Subproblem 2

x + 1 = -7.549834435 Simplifying x + 1 = -7.549834435 Reorder the terms: 1 + x = -7.549834435 Solving 1 + x = -7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -7.549834435 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.549834435 + -1 x = -7.549834435 + -1 Combine like terms: -7.549834435 + -1 = -8.549834435 x = -8.549834435 Simplifying x = -8.549834435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.549834435, -8.549834435}

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