x^2+2x=91

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Solution for x^2+2x=91 equation:


Simplifying
x2 + 2x = 91

Reorder the terms:
2x + x2 = 91

Solving
2x + x2 = 91

Solving for variable 'x'.

Reorder the terms:
-91 + 2x + x2 = 91 + -91

Combine like terms: 91 + -91 = 0
-91 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '91' to each side of the equation.
-91 + 2x + 91 + x2 = 0 + 91

Reorder the terms:
-91 + 91 + 2x + x2 = 0 + 91

Combine like terms: -91 + 91 = 0
0 + 2x + x2 = 0 + 91
2x + x2 = 0 + 91

Combine like terms: 0 + 91 = 91
2x + x2 = 91

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 = 91 + 1

Reorder the terms:
1 + 2x + x2 = 91 + 1

Combine like terms: 91 + 1 = 92
1 + 2x + x2 = 92

Factor a perfect square on the left side:
(x + 1)(x + 1) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(x + 1) equal to 9.591663047 and -9.591663047.

Subproblem 1

x + 1 = 9.591663047 Simplifying x + 1 = 9.591663047 Reorder the terms: 1 + x = 9.591663047 Solving 1 + x = 9.591663047 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 = 9.591663047 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.591663047 + -1 x = 9.591663047 + -1 Combine like terms: 9.591663047 + -1 = 8.591663047 x = 8.591663047 Simplifying x = 8.591663047

Subproblem 2

x + 1 = -9.591663047 Simplifying x + 1 = -9.591663047 Reorder the terms: 1 + x = -9.591663047 Solving 1 + x = -9.591663047 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 = -9.591663047 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.591663047 + -1 x = -9.591663047 + -1 Combine like terms: -9.591663047 + -1 = -10.591663047 x = -10.591663047 Simplifying x = -10.591663047

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.591663047, -10.591663047}

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