2x^2+2x=157

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Solution for 2x^2+2x=157 equation:


Simplifying
2x2 + 2x = 157

Reorder the terms:
2x + 2x2 = 157

Solving
2x + 2x2 = 157

Solving for variable 'x'.

Reorder the terms:
-157 + 2x + 2x2 = 157 + -157

Combine like terms: 157 + -157 = 0
-157 + 2x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-78.5 + x + x2 = 0

Move the constant term to the right:

Add '78.5' to each side of the equation.
-78.5 + x + 78.5 + x2 = 0 + 78.5

Reorder the terms:
-78.5 + 78.5 + x + x2 = 0 + 78.5

Combine like terms: -78.5 + 78.5 = 0.0
0.0 + x + x2 = 0 + 78.5
x + x2 = 0 + 78.5

Combine like terms: 0 + 78.5 = 78.5
x + x2 = 78.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 78.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 78.5 + 0.25

Combine like terms: 78.5 + 0.25 = 78.75
1.25 + x2 = 78.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 78.75

Calculate the square root of the right side: 8.874119675

Break this problem into two subproblems by setting 
(x + 0.5) equal to 8.874119675 and -8.874119675.

Subproblem 1

x + 0.5 = 8.874119675 Simplifying x + 0.5 = 8.874119675 Reorder the terms: 0.5 + x = 8.874119675 Solving 0.5 + x = 8.874119675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 8.874119675 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.874119675 + -0.5 x = 8.874119675 + -0.5 Combine like terms: 8.874119675 + -0.5 = 8.374119675 x = 8.374119675 Simplifying x = 8.374119675

Subproblem 2

x + 0.5 = -8.874119675 Simplifying x + 0.5 = -8.874119675 Reorder the terms: 0.5 + x = -8.874119675 Solving 0.5 + x = -8.874119675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -8.874119675 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.874119675 + -0.5 x = -8.874119675 + -0.5 Combine like terms: -8.874119675 + -0.5 = -9.374119675 x = -9.374119675 Simplifying x = -9.374119675

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.374119675, -9.374119675}

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