8x-16-8x*8x=0

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Solution for 8x-16-8x*8x=0 equation:


Simplifying
8x + -16 + -8x * 8x = 0

Reorder the terms for easier multiplication:
8x + -16 + -8 * 8x * x = 0

Multiply -8 * 8
8x + -16 + -64x * x = 0

Multiply x * x
8x + -16 + -64x2 = 0

Reorder the terms:
-16 + 8x + -64x2 = 0

Solving
-16 + 8x + -64x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + x + -8x2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(-2 + x + -8x2)' equal to zero and attempt to solve: Simplifying -2 + x + -8x2 = 0 Solving -2 + x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.25 + -0.125x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -0.125x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -0.125x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -0.125x + x2 = 0 + -0.25 -0.125x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -0.125x + x2 = -0.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.125x + 0.25 + x2 = -0.25 + 0.25 Reorder the terms: 0.25 + -0.125x + x2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + -0.125x + x2 = 0.00 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 0.5) equal to 0.00 and 0.00.

Subproblem 1

x + 0.5 = 0.00 Simplifying x + 0.5 = 0.00 Reorder the terms: 0.5 + x = 0.00 Solving 0.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.00 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.00 + -0.5 x = 0.00 + -0.5 Combine like terms: 0.00 + -0.5 = -0.5 x = -0.5 Simplifying x = -0.5

Subproblem 2

x + 0.5 = 0.00 Simplifying x + 0.5 = 0.00 Reorder the terms: 0.5 + x = 0.00 Solving 0.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.00 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.00 + -0.5 x = 0.00 + -0.5 Combine like terms: 0.00 + -0.5 = -0.5 x = -0.5 Simplifying x = -0.5

Solution

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

Solution

x = {-0.5, -0.5}

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