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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 = 17562500 14062500 + -7500x + x2 = 17562500 Factor a perfect square on the left side: (x + -3750)(x + -3750) = 17562500 Calculate the square root of the right side: 4190.76365356 Break this problem into two subproblems by setting (x + -3750) equal to 4190.76365356 and -4190.76365356.Subproblem 1
x + -3750 = 4190.76365356 Simplifying x + -3750 = 4190.76365356 Reorder the terms: -3750 + x = 4190.76365356 Solving -3750 + x = 4190.76365356 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 = 4190.76365356 + 3750 Combine like terms: -3750 + 3750 = 0 0 + x = 4190.76365356 + 3750 x = 4190.76365356 + 3750 Combine like terms: 4190.76365356 + 3750 = 7940.76365356 x = 7940.76365356 Simplifying x = 7940.76365356Subproblem 2
x + -3750 = -4190.76365356 Simplifying x + -3750 = -4190.76365356 Reorder the terms: -3750 + x = -4190.76365356 Solving -3750 + x = -4190.76365356 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 = -4190.76365356 + 3750 Combine like terms: -3750 + 3750 = 0 0 + x = -4190.76365356 + 3750 x = -4190.76365356 + 3750 Combine like terms: -4190.76365356 + 3750 = -440.76365356 x = -440.76365356 Simplifying x = -440.76365356Solution
The solution to the problem is based on the solutions from the subproblems. x = {7940.76365356, -440.76365356}
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