2x^2=5+x

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Solution for 2x^2=5+x equation:


Simplifying
2x2 = 5 + x

Solving
2x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-5 + -1x + 2x2 = 5 + x + -5 + -1x

Reorder the terms:
-5 + -1x + 2x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-5 + -1x + 2x2 = 0 + x + -1x
-5 + -1x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-5 + -1x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -0.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -0.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.5x + x2 = 0 + 2.5
-0.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-0.5x + x2 = 2.5

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 = 2.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 2.5 + 0.0625

Combine like terms: 2.5 + 0.0625 = 2.5625
0.0625 + -0.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + -0.25) equal to 1.600781059 and -1.600781059.

Subproblem 1

x + -0.25 = 1.600781059 Simplifying x + -0.25 = 1.600781059 Reorder the terms: -0.25 + x = 1.600781059 Solving -0.25 + x = 1.600781059 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 = 1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.600781059 + 0.25 x = 1.600781059 + 0.25 Combine like terms: 1.600781059 + 0.25 = 1.850781059 x = 1.850781059 Simplifying x = 1.850781059

Subproblem 2

x + -0.25 = -1.600781059 Simplifying x + -0.25 = -1.600781059 Reorder the terms: -0.25 + x = -1.600781059 Solving -0.25 + x = -1.600781059 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 = -1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.600781059 + 0.25 x = -1.600781059 + 0.25 Combine like terms: -1.600781059 + 0.25 = -1.350781059 x = -1.350781059 Simplifying x = -1.350781059

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.850781059, -1.350781059}

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