8x(5-x)=6+2(6x-4)

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Solution for 8x(5-x)=6+2(6x-4) equation:


Simplifying
8x(5 + -1x) = 6 + 2(6x + -4)
(5 * 8x + -1x * 8x) = 6 + 2(6x + -4)
(40x + -8x2) = 6 + 2(6x + -4)

Reorder the terms:
40x + -8x2 = 6 + 2(-4 + 6x)
40x + -8x2 = 6 + (-4 * 2 + 6x * 2)
40x + -8x2 = 6 + (-8 + 12x)

Combine like terms: 6 + -8 = -2
40x + -8x2 = -2 + 12x

Solving
40x + -8x2 = -2 + 12x

Solving for variable 'x'.

Reorder the terms:
2 + 40x + -12x + -8x2 = -2 + 12x + 2 + -12x

Combine like terms: 40x + -12x = 28x
2 + 28x + -8x2 = -2 + 12x + 2 + -12x

Reorder the terms:
2 + 28x + -8x2 = -2 + 2 + 12x + -12x

Combine like terms: -2 + 2 = 0
2 + 28x + -8x2 = 0 + 12x + -12x
2 + 28x + -8x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
2 + 28x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 14x + -4x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + 14x + -4x2)' equal to zero and attempt to solve: Simplifying 1 + 14x + -4x2 = 0 Solving 1 + 14x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -3.5x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -3.5x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -3.5x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -3.5x + x2 = 0 + 0.25 -3.5x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -3.5x + x2 = 0.25 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 0.25 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 0.25 + 3.0625 Combine like terms: 0.25 + 3.0625 = 3.3125 3.0625 + -3.5x + x2 = 3.3125 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 3.3125 Calculate the square root of the right side: 1.820027472 Break this problem into two subproblems by setting (x + -1.75) equal to 1.820027472 and -1.820027472.

Subproblem 1

x + -1.75 = 1.820027472 Simplifying x + -1.75 = 1.820027472 Reorder the terms: -1.75 + x = 1.820027472 Solving -1.75 + x = 1.820027472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.820027472 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.820027472 + 1.75 x = 1.820027472 + 1.75 Combine like terms: 1.820027472 + 1.75 = 3.570027472 x = 3.570027472 Simplifying x = 3.570027472

Subproblem 2

x + -1.75 = -1.820027472 Simplifying x + -1.75 = -1.820027472 Reorder the terms: -1.75 + x = -1.820027472 Solving -1.75 + x = -1.820027472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.820027472 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.820027472 + 1.75 x = -1.820027472 + 1.75 Combine like terms: -1.820027472 + 1.75 = -0.070027472 x = -0.070027472 Simplifying x = -0.070027472

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.570027472, -0.070027472}

Solution

x = {3.570027472, -0.070027472}

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