80=(4-4x)(10-4x)

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Solution for 80=(4-4x)(10-4x) equation:


Simplifying
80 = (4 + -4x)(10 + -4x)

Multiply (4 + -4x) * (10 + -4x)
80 = (4(10 + -4x) + -4x * (10 + -4x))
80 = ((10 * 4 + -4x * 4) + -4x * (10 + -4x))
80 = ((40 + -16x) + -4x * (10 + -4x))
80 = (40 + -16x + (10 * -4x + -4x * -4x))
80 = (40 + -16x + (-40x + 16x2))

Combine like terms: -16x + -40x = -56x
80 = (40 + -56x + 16x2)

Solving
80 = 40 + -56x + 16x2

Solving for variable 'x'.

Combine like terms: 80 + -40 = 40
40 + 56x + -16x2 = 40 + -56x + 16x2 + -40 + 56x + -16x2

Reorder the terms:
40 + 56x + -16x2 = 40 + -40 + -56x + 56x + 16x2 + -16x2

Combine like terms: 40 + -40 = 0
40 + 56x + -16x2 = 0 + -56x + 56x + 16x2 + -16x2
40 + 56x + -16x2 = -56x + 56x + 16x2 + -16x2

Combine like terms: -56x + 56x = 0
40 + 56x + -16x2 = 0 + 16x2 + -16x2
40 + 56x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
40 + 56x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + 7x + -2x2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(5 + 7x + -2x2)' equal to zero and attempt to solve: Simplifying 5 + 7x + -2x2 = 0 Solving 5 + 7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.5x + x2 = 0 + 2.5 -3.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.5x + x2 = 2.5 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 = 2.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 2.5 + 3.0625 Combine like terms: 2.5 + 3.0625 = 5.5625 3.0625 + -3.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + -1.75) equal to 2.358495283 and -2.358495283.

Subproblem 1

x + -1.75 = 2.358495283 Simplifying x + -1.75 = 2.358495283 Reorder the terms: -1.75 + x = 2.358495283 Solving -1.75 + x = 2.358495283 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 = 2.358495283 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.358495283 + 1.75 x = 2.358495283 + 1.75 Combine like terms: 2.358495283 + 1.75 = 4.108495283 x = 4.108495283 Simplifying x = 4.108495283

Subproblem 2

x + -1.75 = -2.358495283 Simplifying x + -1.75 = -2.358495283 Reorder the terms: -1.75 + x = -2.358495283 Solving -1.75 + x = -2.358495283 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 = -2.358495283 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.358495283 + 1.75 x = -2.358495283 + 1.75 Combine like terms: -2.358495283 + 1.75 = -0.608495283 x = -0.608495283 Simplifying x = -0.608495283

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.108495283, -0.608495283}

Solution

x = {4.108495283, -0.608495283}

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