x^2-51=-2x

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Solution for x^2-51=-2x equation:


Simplifying
x2 + -51 = -2x

Reorder the terms:
-51 + x2 = -2x

Solving
-51 + x2 = -2x

Solving for variable 'x'.

Reorder the terms:
-51 + 2x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-51 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + 2x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + 2x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 2x + x2 = 0 + 51
2x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
2x + x2 = 51

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 = 51 + 1

Reorder the terms:
1 + 2x + x2 = 51 + 1

Combine like terms: 51 + 1 = 52
1 + 2x + x2 = 52

Factor a perfect square on the left side:
(x + 1)(x + 1) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + 1) equal to 7.211102551 and -7.211102551.

Subproblem 1

x + 1 = 7.211102551 Simplifying x + 1 = 7.211102551 Reorder the terms: 1 + x = 7.211102551 Solving 1 + x = 7.211102551 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 = 7.211102551 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.211102551 + -1 x = 7.211102551 + -1 Combine like terms: 7.211102551 + -1 = 6.211102551 x = 6.211102551 Simplifying x = 6.211102551

Subproblem 2

x + 1 = -7.211102551 Simplifying x + 1 = -7.211102551 Reorder the terms: 1 + x = -7.211102551 Solving 1 + x = -7.211102551 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 = -7.211102551 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.211102551 + -1 x = -7.211102551 + -1 Combine like terms: -7.211102551 + -1 = -8.211102551 x = -8.211102551 Simplifying x = -8.211102551

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.211102551, -8.211102551}

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