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Simplifying 480 = 480x + -2x2 Solving 480 = 480x + -2x2 Solving for variable 'x'. Reorder the terms: 480 + -480x + 2x2 = 480x + -480x + -2x2 + 2x2 Combine like terms: 480x + -480x = 0 480 + -480x + 2x2 = 0 + -2x2 + 2x2 480 + -480x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 480 + -480x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(240 + -240x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(240 + -240x + x2)' equal to zero and attempt to solve: Simplifying 240 + -240x + x2 = 0 Solving 240 + -240x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-240' to each side of the equation. 240 + -240x + -240 + x2 = 0 + -240 Reorder the terms: 240 + -240 + -240x + x2 = 0 + -240 Combine like terms: 240 + -240 = 0 0 + -240x + x2 = 0 + -240 -240x + x2 = 0 + -240 Combine like terms: 0 + -240 = -240 -240x + x2 = -240 The x term is -240x. Take half its coefficient (-120). Square it (14400) and add it to both sides. Add '14400' to each side of the equation. -240x + 14400 + x2 = -240 + 14400 Reorder the terms: 14400 + -240x + x2 = -240 + 14400 Combine like terms: -240 + 14400 = 14160 14400 + -240x + x2 = 14160 Factor a perfect square on the left side: (x + -120)(x + -120) = 14160 Calculate the square root of the right side: 118.995798245 Break this problem into two subproblems by setting (x + -120) equal to 118.995798245 and -118.995798245.Subproblem 1
x + -120 = 118.995798245 Simplifying x + -120 = 118.995798245 Reorder the terms: -120 + x = 118.995798245 Solving -120 + x = 118.995798245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + x = 118.995798245 + 120 Combine like terms: -120 + 120 = 0 0 + x = 118.995798245 + 120 x = 118.995798245 + 120 Combine like terms: 118.995798245 + 120 = 238.995798245 x = 238.995798245 Simplifying x = 238.995798245Subproblem 2
x + -120 = -118.995798245 Simplifying x + -120 = -118.995798245 Reorder the terms: -120 + x = -118.995798245 Solving -120 + x = -118.995798245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + x = -118.995798245 + 120 Combine like terms: -120 + 120 = 0 0 + x = -118.995798245 + 120 x = -118.995798245 + 120 Combine like terms: -118.995798245 + 120 = 1.004201755 x = 1.004201755 Simplifying x = 1.004201755Solution
The solution to the problem is based on the solutions from the subproblems. x = {238.995798245, 1.004201755}Solution
x = {238.995798245, 1.004201755}
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