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Simplifying 0.08x2 + 120x + -80 = 0 Reorder the terms: -80 + 120x + 0.08x2 = 0 Solving -80 + 120x + 0.08x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. -1000 + 1500x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 1500x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 1500x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 1500x + x2 = 0 + 1000 1500x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 1500x + x2 = 1000 The x term is 1500x. Take half its coefficient (750). Square it (562500) and add it to both sides. Add '562500' to each side of the equation. 1500x + 562500 + x2 = 1000 + 562500 Reorder the terms: 562500 + 1500x + x2 = 1000 + 562500 Combine like terms: 1000 + 562500 = 563500 562500 + 1500x + x2 = 563500 Factor a perfect square on the left side: (x + 750)(x + 750) = 563500 Calculate the square root of the right side: 750.666370633 Break this problem into two subproblems by setting (x + 750) equal to 750.666370633 and -750.666370633.Subproblem 1
x + 750 = 750.666370633 Simplifying x + 750 = 750.666370633 Reorder the terms: 750 + x = 750.666370633 Solving 750 + x = 750.666370633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-750' to each side of the equation. 750 + -750 + x = 750.666370633 + -750 Combine like terms: 750 + -750 = 0 0 + x = 750.666370633 + -750 x = 750.666370633 + -750 Combine like terms: 750.666370633 + -750 = 0.666370633 x = 0.666370633 Simplifying x = 0.666370633Subproblem 2
x + 750 = -750.666370633 Simplifying x + 750 = -750.666370633 Reorder the terms: 750 + x = -750.666370633 Solving 750 + x = -750.666370633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-750' to each side of the equation. 750 + -750 + x = -750.666370633 + -750 Combine like terms: 750 + -750 = 0 0 + x = -750.666370633 + -750 x = -750.666370633 + -750 Combine like terms: -750.666370633 + -750 = -1500.666370633 x = -1500.666370633 Simplifying x = -1500.666370633Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.666370633, -1500.666370633}
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