2x^2-x=63

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


Simplifying
2x2 + -1x = 63

Reorder the terms:
-1x + 2x2 = 63

Solving
-1x + 2x2 = 63

Solving for variable 'x'.

Reorder the terms:
-63 + -1x + 2x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-63 + -1x + 2x2 = 0

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

Divide each side by '2'.
-31.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '31.5' to each side of the equation.
-31.5 + -0.5x + 31.5 + x2 = 0 + 31.5

Reorder the terms:
-31.5 + 31.5 + -0.5x + x2 = 0 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + -0.5x + x2 = 0 + 31.5
-0.5x + x2 = 0 + 31.5

Combine like terms: 0 + 31.5 = 31.5
-0.5x + x2 = 31.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 31.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 31.5 + 0.0625

Combine like terms: 31.5 + 0.0625 = 31.5625
0.0625 + -0.5x + x2 = 31.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 31.5625

Calculate the square root of the right side: 5.618051264

Break this problem into two subproblems by setting 
(x + -0.25) equal to 5.618051264 and -5.618051264.

Subproblem 1

x + -0.25 = 5.618051264 Simplifying x + -0.25 = 5.618051264 Reorder the terms: -0.25 + x = 5.618051264 Solving -0.25 + x = 5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 5.618051264 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 5.618051264 + 0.25 x = 5.618051264 + 0.25 Combine like terms: 5.618051264 + 0.25 = 5.868051264 x = 5.868051264 Simplifying x = 5.868051264

Subproblem 2

x + -0.25 = -5.618051264 Simplifying x + -0.25 = -5.618051264 Reorder the terms: -0.25 + x = -5.618051264 Solving -0.25 + x = -5.618051264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -5.618051264 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -5.618051264 + 0.25 x = -5.618051264 + 0.25 Combine like terms: -5.618051264 + 0.25 = -5.368051264 x = -5.368051264 Simplifying x = -5.368051264

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.868051264, -5.368051264}

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