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Simplifying -0.02x2 + 150x + -70000 = 0 Reorder the terms: -70000 + 150x + -0.02x2 = 0 Solving -70000 + 150x + -0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 3500000 + -7500x + x2 = 0 Move the constant term to the right: Add '-3500000' to each side of the equation. 3500000 + -7500x + -3500000 + x2 = 0 + -3500000 Reorder the terms: 3500000 + -3500000 + -7500x + x2 = 0 + -3500000 Combine like terms: 3500000 + -3500000 = 0 0 + -7500x + x2 = 0 + -3500000 -7500x + x2 = 0 + -3500000 Combine like terms: 0 + -3500000 = -3500000 -7500x + x2 = -3500000 The x term is -7500x. Take half its coefficient (-3750). Square it (14062500) and add it to both sides. Add '14062500' to each side of the equation. -7500x + 14062500 + x2 = -3500000 + 14062500 Reorder the terms: 14062500 + -7500x + x2 = -3500000 + 14062500 Combine like terms: -3500000 + 14062500 = 10562500 14062500 + -7500x + x2 = 10562500 Factor a perfect square on the left side: (x + -3750)(x + -3750) = 10562500 Calculate the square root of the right side: 3250 Break this problem into two subproblems by setting (x + -3750) equal to 3250 and -3250.Subproblem 1
x + -3750 = 3250 Simplifying x + -3750 = 3250 Reorder the terms: -3750 + x = 3250 Solving -3750 + x = 3250 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3750' to each side of the equation. -3750 + 3750 + x = 3250 + 3750 Combine like terms: -3750 + 3750 = 0 0 + x = 3250 + 3750 x = 3250 + 3750 Combine like terms: 3250 + 3750 = 7000 x = 7000 Simplifying x = 7000Subproblem 2
x + -3750 = -3250 Simplifying x + -3750 = -3250 Reorder the terms: -3750 + x = -3250 Solving -3750 + x = -3250 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3750' to each side of the equation. -3750 + 3750 + x = -3250 + 3750 Combine like terms: -3750 + 3750 = 0 0 + x = -3250 + 3750 x = -3250 + 3750 Combine like terms: -3250 + 3750 = 500 x = 500 Simplifying x = 500Solution
The solution to the problem is based on the solutions from the subproblems. x = {7000, 500}
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