x^2+2x-50=0

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Solution for x^2+2x-50=0 equation:


Simplifying
x2 + 2x + -50 = 0

Reorder the terms:
-50 + 2x + x2 = 0

Solving
-50 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 2x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 2x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 2x + x2 = 0 + 50
2x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
2x + x2 = 50

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 = 50 + 1

Reorder the terms:
1 + 2x + x2 = 50 + 1

Combine like terms: 50 + 1 = 51
1 + 2x + x2 = 51

Factor a perfect square on the left side:
(x + 1)(x + 1) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + 1) equal to 7.141428429 and -7.141428429.

Subproblem 1

x + 1 = 7.141428429 Simplifying x + 1 = 7.141428429 Reorder the terms: 1 + x = 7.141428429 Solving 1 + x = 7.141428429 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 = 7.141428429 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.141428429 + -1 x = 7.141428429 + -1 Combine like terms: 7.141428429 + -1 = 6.141428429 x = 6.141428429 Simplifying x = 6.141428429

Subproblem 2

x + 1 = -7.141428429 Simplifying x + 1 = -7.141428429 Reorder the terms: 1 + x = -7.141428429 Solving 1 + x = -7.141428429 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 = -7.141428429 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.141428429 + -1 x = -7.141428429 + -1 Combine like terms: -7.141428429 + -1 = -8.141428429 x = -8.141428429 Simplifying x = -8.141428429

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.141428429, -8.141428429}

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