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Simplifying -16x2 + 1920x + 51200 = 0 Reorder the terms: 51200 + 1920x + -16x2 = 0 Solving 51200 + 1920x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(3200 + 120x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3200 + 120x + -1x2)' equal to zero and attempt to solve: Simplifying 3200 + 120x + -1x2 = 0 Solving 3200 + 120x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3200 + -120x + x2 = 0 Move the constant term to the right: Add '3200' to each side of the equation. -3200 + -120x + 3200 + x2 = 0 + 3200 Reorder the terms: -3200 + 3200 + -120x + x2 = 0 + 3200 Combine like terms: -3200 + 3200 = 0 0 + -120x + x2 = 0 + 3200 -120x + x2 = 0 + 3200 Combine like terms: 0 + 3200 = 3200 -120x + x2 = 3200 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = 3200 + 3600 Reorder the terms: 3600 + -120x + x2 = 3200 + 3600 Combine like terms: 3200 + 3600 = 6800 3600 + -120x + x2 = 6800 Factor a perfect square on the left side: (x + -60)(x + -60) = 6800 Calculate the square root of the right side: 82.462112512 Break this problem into two subproblems by setting (x + -60) equal to 82.462112512 and -82.462112512.Subproblem 1
x + -60 = 82.462112512 Simplifying x + -60 = 82.462112512 Reorder the terms: -60 + x = 82.462112512 Solving -60 + x = 82.462112512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 82.462112512 + 60 Combine like terms: -60 + 60 = 0 0 + x = 82.462112512 + 60 x = 82.462112512 + 60 Combine like terms: 82.462112512 + 60 = 142.462112512 x = 142.462112512 Simplifying x = 142.462112512Subproblem 2
x + -60 = -82.462112512 Simplifying x + -60 = -82.462112512 Reorder the terms: -60 + x = -82.462112512 Solving -60 + x = -82.462112512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -82.462112512 + 60 Combine like terms: -60 + 60 = 0 0 + x = -82.462112512 + 60 x = -82.462112512 + 60 Combine like terms: -82.462112512 + 60 = -22.462112512 x = -22.462112512 Simplifying x = -22.462112512Solution
The solution to the problem is based on the solutions from the subproblems. x = {142.462112512, -22.462112512}Solution
x = {142.462112512, -22.462112512}
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