.25x^2-8=x

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Solution for .25x^2-8=x equation:


Simplifying
0.25x2 + -8 = x

Reorder the terms:
-8 + 0.25x2 = x

Solving
-8 + 0.25x2 = x

Solving for variable 'x'.

Reorder the terms:
-8 + -1x + 0.25x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + -1x + 0.25x2 = 0

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

Divide each side by '0.25'.
-32 + -4x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -4x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -4x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -4x + x2 = 0 + 32
-4x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-4x + x2 = 32

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 32 + 4

Reorder the terms:
4 + -4x + x2 = 32 + 4

Combine like terms: 32 + 4 = 36
4 + -4x + x2 = 36

Factor a perfect square on the left side:
(x + -2)(x + -2) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + -2) equal to 6 and -6.

Subproblem 1

x + -2 = 6 Simplifying x + -2 = 6 Reorder the terms: -2 + x = 6 Solving -2 + x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 6 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6 + 2 x = 6 + 2 Combine like terms: 6 + 2 = 8 x = 8 Simplifying x = 8

Subproblem 2

x + -2 = -6 Simplifying x + -2 = -6 Reorder the terms: -2 + x = -6 Solving -2 + x = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -6 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6 + 2 x = -6 + 2 Combine like terms: -6 + 2 = -4 x = -4 Simplifying x = -4

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8, -4}

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