20=2x(10-4x)

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Solution for 20=2x(10-4x) equation:


Simplifying
20 = 2x(10 + -4x)
20 = (10 * 2x + -4x * 2x)
20 = (20x + -8x2)

Solving
20 = 20x + -8x2

Solving for variable 'x'.

Reorder the terms:
20 + -20x + 8x2 = 20x + -20x + -8x2 + 8x2

Combine like terms: 20x + -20x = 0
20 + -20x + 8x2 = 0 + -8x2 + 8x2
20 + -20x + 8x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
20 + -20x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -5x + 2x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(5 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + -5x + 2x2 = 0 Solving 5 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -2.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -2.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -2.5x + x2 = 0 + -2.5 -2.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -2.5x + x2 = -2.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -2.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -2.5 + 1.5625 Combine like terms: -2.5 + 1.5625 = -0.9375 1.5625 + -2.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -0.9375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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