784=(40-2x)(20-2x)

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Solution for 784=(40-2x)(20-2x) equation:


Simplifying
784 = (40 + -2x)(20 + -2x)

Multiply (40 + -2x) * (20 + -2x)
784 = (40(20 + -2x) + -2x * (20 + -2x))
784 = ((20 * 40 + -2x * 40) + -2x * (20 + -2x))
784 = ((800 + -80x) + -2x * (20 + -2x))
784 = (800 + -80x + (20 * -2x + -2x * -2x))
784 = (800 + -80x + (-40x + 4x2))

Combine like terms: -80x + -40x = -120x
784 = (800 + -120x + 4x2)

Solving
784 = 800 + -120x + 4x2

Solving for variable 'x'.

Combine like terms: 784 + -800 = -16
-16 + 120x + -4x2 = 800 + -120x + 4x2 + -800 + 120x + -4x2

Reorder the terms:
-16 + 120x + -4x2 = 800 + -800 + -120x + 120x + 4x2 + -4x2

Combine like terms: 800 + -800 = 0
-16 + 120x + -4x2 = 0 + -120x + 120x + 4x2 + -4x2
-16 + 120x + -4x2 = -120x + 120x + 4x2 + -4x2

Combine like terms: -120x + 120x = 0
-16 + 120x + -4x2 = 0 + 4x2 + -4x2
-16 + 120x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-16 + 120x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 30x + -1x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-4 + 30x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + 30x + -1x2 = 0 Solving -4 + 30x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -30x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -30x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -30x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -30x + x2 = 0 + -4 -30x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -30x + x2 = -4 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -4 + 225 Reorder the terms: 225 + -30x + x2 = -4 + 225 Combine like terms: -4 + 225 = 221 225 + -30x + x2 = 221 Factor a perfect square on the left side: (x + -15)(x + -15) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (x + -15) equal to 14.866068747 and -14.866068747.

Subproblem 1

x + -15 = 14.866068747 Simplifying x + -15 = 14.866068747 Reorder the terms: -15 + x = 14.866068747 Solving -15 + x = 14.866068747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 14.866068747 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.866068747 + 15 x = 14.866068747 + 15 Combine like terms: 14.866068747 + 15 = 29.866068747 x = 29.866068747 Simplifying x = 29.866068747

Subproblem 2

x + -15 = -14.866068747 Simplifying x + -15 = -14.866068747 Reorder the terms: -15 + x = -14.866068747 Solving -15 + x = -14.866068747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -14.866068747 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.866068747 + 15 x = -14.866068747 + 15 Combine like terms: -14.866068747 + 15 = 0.133931253 x = 0.133931253 Simplifying x = 0.133931253

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.866068747, 0.133931253}

Solution

x = {29.866068747, 0.133931253}

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