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Simplifying (20 + 2x)(10 + 20x) = 1064 Multiply (20 + 2x) * (10 + 20x) (20(10 + 20x) + 2x * (10 + 20x)) = 1064 ((10 * 20 + 20x * 20) + 2x * (10 + 20x)) = 1064 ((200 + 400x) + 2x * (10 + 20x)) = 1064 (200 + 400x + (10 * 2x + 20x * 2x)) = 1064 (200 + 400x + (20x + 40x2)) = 1064 Combine like terms: 400x + 20x = 420x (200 + 420x + 40x2) = 1064 Solving 200 + 420x + 40x2 = 1064 Solving for variable 'x'. Reorder the terms: 200 + -1064 + 420x + 40x2 = 1064 + -1064 Combine like terms: 200 + -1064 = -864 -864 + 420x + 40x2 = 1064 + -1064 Combine like terms: 1064 + -1064 = 0 -864 + 420x + 40x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-216 + 105x + 10x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-216 + 105x + 10x2)' equal to zero and attempt to solve: Simplifying -216 + 105x + 10x2 = 0 Solving -216 + 105x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -21.6 + 10.5x + x2 = 0.0 Move the constant term to the right: Add '21.6' to each side of the equation. -21.6 + 10.5x + 21.6 + x2 = 0.0 + 21.6 Reorder the terms: -21.6 + 21.6 + 10.5x + x2 = 0.0 + 21.6 Combine like terms: -21.6 + 21.6 = 0.0 0.0 + 10.5x + x2 = 0.0 + 21.6 10.5x + x2 = 0.0 + 21.6 Combine like terms: 0.0 + 21.6 = 21.6 10.5x + x2 = 21.6 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 21.6 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 21.6 + 27.5625 Combine like terms: 21.6 + 27.5625 = 49.1625 27.5625 + 10.5x + x2 = 49.1625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 49.1625 Calculate the square root of the right side: 7.011597536 Break this problem into two subproblems by setting (x + 5.25) equal to 7.011597536 and -7.011597536.Subproblem 1
x + 5.25 = 7.011597536 Simplifying x + 5.25 = 7.011597536 Reorder the terms: 5.25 + x = 7.011597536 Solving 5.25 + x = 7.011597536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 7.011597536 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 7.011597536 + -5.25 x = 7.011597536 + -5.25 Combine like terms: 7.011597536 + -5.25 = 1.761597536 x = 1.761597536 Simplifying x = 1.761597536Subproblem 2
x + 5.25 = -7.011597536 Simplifying x + 5.25 = -7.011597536 Reorder the terms: 5.25 + x = -7.011597536 Solving 5.25 + x = -7.011597536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -7.011597536 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -7.011597536 + -5.25 x = -7.011597536 + -5.25 Combine like terms: -7.011597536 + -5.25 = -12.261597536 x = -12.261597536 Simplifying x = -12.261597536Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.761597536, -12.261597536}Solution
x = {1.761597536, -12.261597536}
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