x^2+10x-57=

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Solution for x^2+10x-57= equation:


Simplifying
x2 + 10x + -57 = 0

Reorder the terms:
-57 + 10x + x2 = 0

Solving
-57 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + 10x + 57 + x2 = 0 + 57

Reorder the terms:
-57 + 57 + 10x + x2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + 10x + x2 = 0 + 57
10x + x2 = 0 + 57

Combine like terms: 0 + 57 = 57
10x + x2 = 57

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 57 + 25

Reorder the terms:
25 + 10x + x2 = 57 + 25

Combine like terms: 57 + 25 = 82
25 + 10x + x2 = 82

Factor a perfect square on the left side:
(x + 5)(x + 5) = 82

Calculate the square root of the right side: 9.055385138

Break this problem into two subproblems by setting 
(x + 5) equal to 9.055385138 and -9.055385138.

Subproblem 1

x + 5 = 9.055385138 Simplifying x + 5 = 9.055385138 Reorder the terms: 5 + x = 9.055385138 Solving 5 + x = 9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 9.055385138 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.055385138 + -5 x = 9.055385138 + -5 Combine like terms: 9.055385138 + -5 = 4.055385138 x = 4.055385138 Simplifying x = 4.055385138

Subproblem 2

x + 5 = -9.055385138 Simplifying x + 5 = -9.055385138 Reorder the terms: 5 + x = -9.055385138 Solving 5 + x = -9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -9.055385138 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.055385138 + -5 x = -9.055385138 + -5 Combine like terms: -9.055385138 + -5 = -14.055385138 x = -14.055385138 Simplifying x = -14.055385138

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.055385138, -14.055385138}

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