x^2+2x-190=

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Solution for x^2+2x-190= equation:


Simplifying
x2 + 2x + -190 = 0

Reorder the terms:
-190 + 2x + x2 = 0

Solving
-190 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '190' to each side of the equation.
-190 + 2x + 190 + x2 = 0 + 190

Reorder the terms:
-190 + 190 + 2x + x2 = 0 + 190

Combine like terms: -190 + 190 = 0
0 + 2x + x2 = 0 + 190
2x + x2 = 0 + 190

Combine like terms: 0 + 190 = 190
2x + x2 = 190

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 = 190 + 1

Reorder the terms:
1 + 2x + x2 = 190 + 1

Combine like terms: 190 + 1 = 191
1 + 2x + x2 = 191

Factor a perfect square on the left side:
(x + 1)(x + 1) = 191

Calculate the square root of the right side: 13.820274961

Break this problem into two subproblems by setting 
(x + 1) equal to 13.820274961 and -13.820274961.

Subproblem 1

x + 1 = 13.820274961 Simplifying x + 1 = 13.820274961 Reorder the terms: 1 + x = 13.820274961 Solving 1 + x = 13.820274961 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 = 13.820274961 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.820274961 + -1 x = 13.820274961 + -1 Combine like terms: 13.820274961 + -1 = 12.820274961 x = 12.820274961 Simplifying x = 12.820274961

Subproblem 2

x + 1 = -13.820274961 Simplifying x + 1 = -13.820274961 Reorder the terms: 1 + x = -13.820274961 Solving 1 + x = -13.820274961 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 = -13.820274961 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.820274961 + -1 x = -13.820274961 + -1 Combine like terms: -13.820274961 + -1 = -14.820274961 x = -14.820274961 Simplifying x = -14.820274961

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.820274961, -14.820274961}

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