4x-0.5x^2=8

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Solution for 4x-0.5x^2=8 equation:


Simplifying
4x + -0.5x2 = 8

Solving
4x + -0.5x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 4x + -0.5x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 4x + -0.5x2 = 0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
16 + -8x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -8x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -8x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -8x + x2 = 0 + -16
-8x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-8x + x2 = -16

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -16 + 16

Reorder the terms:
16 + -8x + x2 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + -8x + x2 = 0

Factor a perfect square on the left side:
(x + -4)(x + -4) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + -4) equal to 0 and 0.

Subproblem 1

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

Subproblem 2

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

Solution

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

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