2x^2=0.5x+0.75

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Solution for 2x^2=0.5x+0.75 equation:


Simplifying
2x2 = 0.5x + 0.75

Reorder the terms:
2x2 = 0.75 + 0.5x

Solving
2x2 = 0.75 + 0.5x

Solving for variable 'x'.

Reorder the terms:
-0.75 + -0.5x + 2x2 = 0.75 + 0.5x + -0.75 + -0.5x

Reorder the terms:
-0.75 + -0.5x + 2x2 = 0.75 + -0.75 + 0.5x + -0.5x

Combine like terms: 0.75 + -0.75 = 0.00
-0.75 + -0.5x + 2x2 = 0.00 + 0.5x + -0.5x
-0.75 + -0.5x + 2x2 = 0.5x + -0.5x

Combine like terms: 0.5x + -0.5x = 0.0
-0.75 + -0.5x + 2x2 = 0.0

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

Divide each side by '2'.
-0.375 + -0.25x + x2 = 0.0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -0.25x + 0.375 + x2 = 0.0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -0.25x + x2 = 0.0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -0.25x + x2 = 0.0 + 0.375
-0.25x + x2 = 0.0 + 0.375

Combine like terms: 0.0 + 0.375 = 0.375
-0.25x + x2 = 0.375

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 0.375 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 0.375 + 0.015625

Combine like terms: 0.375 + 0.015625 = 0.390625
0.015625 + -0.25x + x2 = 0.390625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.390625

Calculate the square root of the right side: 0.625

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.625 and -0.625.

Subproblem 1

x + -0.125 = 0.625 Simplifying x + -0.125 = 0.625 Reorder the terms: -0.125 + x = 0.625 Solving -0.125 + x = 0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.625 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.625 + 0.125 x = 0.625 + 0.125 Combine like terms: 0.625 + 0.125 = 0.75 x = 0.75 Simplifying x = 0.75

Subproblem 2

x + -0.125 = -0.625 Simplifying x + -0.125 = -0.625 Reorder the terms: -0.125 + x = -0.625 Solving -0.125 + x = -0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.625 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.625 + 0.125 x = -0.625 + 0.125 Combine like terms: -0.625 + 0.125 = -0.5 x = -0.5 Simplifying x = -0.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.75, -0.5}

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