2x^2+2x=63

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Solution for 2x^2+2x=63 equation:


Simplifying
2x2 + 2x = 63

Reorder the terms:
2x + 2x2 = 63

Solving
2x + 2x2 = 63

Solving for variable 'x'.

Reorder the terms:
-63 + 2x + 2x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-63 + 2x + 2x2 = 0

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

Divide each side by '2'.
-31.5 + x + x2 = 0

Move the constant term to the right:

Add '31.5' to each side of the equation.
-31.5 + x + 31.5 + x2 = 0 + 31.5

Reorder the terms:
-31.5 + 31.5 + x + x2 = 0 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + x + x2 = 0 + 31.5
x + x2 = 0 + 31.5

Combine like terms: 0 + 31.5 = 31.5
x + x2 = 31.5

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 = 31.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 31.5 + 0.25

Combine like terms: 31.5 + 0.25 = 31.75
1.25 + x2 = 31.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 31.75

Calculate the square root of the right side: 5.634713835

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.634713835 and -5.634713835.

Subproblem 1

x + 0.5 = 5.634713835 Simplifying x + 0.5 = 5.634713835 Reorder the terms: 0.5 + x = 5.634713835 Solving 0.5 + x = 5.634713835 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 = 5.634713835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.634713835 + -0.5 x = 5.634713835 + -0.5 Combine like terms: 5.634713835 + -0.5 = 5.134713835 x = 5.134713835 Simplifying x = 5.134713835

Subproblem 2

x + 0.5 = -5.634713835 Simplifying x + 0.5 = -5.634713835 Reorder the terms: 0.5 + x = -5.634713835 Solving 0.5 + x = -5.634713835 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 = -5.634713835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.634713835 + -0.5 x = -5.634713835 + -0.5 Combine like terms: -5.634713835 + -0.5 = -6.134713835 x = -6.134713835 Simplifying x = -6.134713835

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.134713835, -6.134713835}

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