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Simplifying -500x2 + 5.97 * 5.02(120 + -1x) + 4.75 * 120(150 + -1x) = 0 Multiply 5.97 * 5.02 -500x2 + 29.9694(120 + -1x) + 4.75 * 120(150 + -1x) = 0 -500x2 + (120 * 29.9694 + -1x * 29.9694) + 4.75 * 120(150 + -1x) = 0 -500x2 + (3596.328 + -29.9694x) + 4.75 * 120(150 + -1x) = 0 Multiply 4.75 * 120 -500x2 + 3596.328 + -29.9694x + 570(150 + -1x) = 0 -500x2 + 3596.328 + -29.9694x + (150 * 570 + -1x * 570) = 0 -500x2 + 3596.328 + -29.9694x + (85500 + -570x) = 0 Reorder the terms: 3596.328 + 85500 + -29.9694x + -570x + -500x2 = 0 Combine like terms: 3596.328 + 85500 = 89096.328 89096.328 + -29.9694x + -570x + -500x2 = 0 Combine like terms: -29.9694x + -570x = -599.9694x 89096.328 + -599.9694x + -500x2 = 0 Solving 89096.328 + -599.9694x + -500x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -500 the coefficient of the squared term: Divide each side by '-500'. -178.192656 + 1.1999388x + x2 = 0 Move the constant term to the right: Add '178.192656' to each side of the equation. -178.192656 + 1.1999388x + 178.192656 + x2 = 0 + 178.192656 Reorder the terms: -178.192656 + 178.192656 + 1.1999388x + x2 = 0 + 178.192656 Combine like terms: -178.192656 + 178.192656 = 0.000000 0.000000 + 1.1999388x + x2 = 0 + 178.192656 1.1999388x + x2 = 0 + 178.192656 Combine like terms: 0 + 178.192656 = 178.192656 1.1999388x + x2 = 178.192656 The x term is 1.1999388x. Take half its coefficient (0.5999694). Square it (0.3599632809) and add it to both sides. Add '0.3599632809' to each side of the equation. 1.1999388x + 0.3599632809 + x2 = 178.192656 + 0.3599632809 Reorder the terms: 0.3599632809 + 1.1999388x + x2 = 178.192656 + 0.3599632809 Combine like terms: 178.192656 + 0.3599632809 = 178.5526192809 0.3599632809 + 1.1999388x + x2 = 178.5526192809 Factor a perfect square on the left side: (x + 0.5999694)(x + 0.5999694) = 178.5526192809 Calculate the square root of the right side: 13.362358298 Break this problem into two subproblems by setting (x + 0.5999694) equal to 13.362358298 and -13.362358298.Subproblem 1
x + 0.5999694 = 13.362358298 Simplifying x + 0.5999694 = 13.362358298 Reorder the terms: 0.5999694 + x = 13.362358298 Solving 0.5999694 + x = 13.362358298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5999694' to each side of the equation. 0.5999694 + -0.5999694 + x = 13.362358298 + -0.5999694 Combine like terms: 0.5999694 + -0.5999694 = 0.0000000 0.0000000 + x = 13.362358298 + -0.5999694 x = 13.362358298 + -0.5999694 Combine like terms: 13.362358298 + -0.5999694 = 12.762388898 x = 12.762388898 Simplifying x = 12.762388898Subproblem 2
x + 0.5999694 = -13.362358298 Simplifying x + 0.5999694 = -13.362358298 Reorder the terms: 0.5999694 + x = -13.362358298 Solving 0.5999694 + x = -13.362358298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5999694' to each side of the equation. 0.5999694 + -0.5999694 + x = -13.362358298 + -0.5999694 Combine like terms: 0.5999694 + -0.5999694 = 0.0000000 0.0000000 + x = -13.362358298 + -0.5999694 x = -13.362358298 + -0.5999694 Combine like terms: -13.362358298 + -0.5999694 = -13.962327698 x = -13.962327698 Simplifying x = -13.962327698Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.762388898, -13.962327698}
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