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Simplifying 0 = 70 + 2x + -0.02x2 Solving 0 = 70 + 2x + -0.02x2 Solving for variable 'x'. Combine like terms: 0 + -70 = -70 -70 + -2x + 0.02x2 = 70 + 2x + -0.02x2 + -70 + -2x + 0.02x2 Reorder the terms: -70 + -2x + 0.02x2 = 70 + -70 + 2x + -2x + -0.02x2 + 0.02x2 Combine like terms: 70 + -70 = 0 -70 + -2x + 0.02x2 = 0 + 2x + -2x + -0.02x2 + 0.02x2 -70 + -2x + 0.02x2 = 2x + -2x + -0.02x2 + 0.02x2 Combine like terms: 2x + -2x = 0 -70 + -2x + 0.02x2 = 0 + -0.02x2 + 0.02x2 -70 + -2x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 -70 + -2x + 0.02x2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -3500 + -100x + x2 = 0 Move the constant term to the right: Add '3500' to each side of the equation. -3500 + -100x + 3500 + x2 = 0 + 3500 Reorder the terms: -3500 + 3500 + -100x + x2 = 0 + 3500 Combine like terms: -3500 + 3500 = 0 0 + -100x + x2 = 0 + 3500 -100x + x2 = 0 + 3500 Combine like terms: 0 + 3500 = 3500 -100x + x2 = 3500 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = 3500 + 2500 Reorder the terms: 2500 + -100x + x2 = 3500 + 2500 Combine like terms: 3500 + 2500 = 6000 2500 + -100x + x2 = 6000 Factor a perfect square on the left side: (x + -50)(x + -50) = 6000 Calculate the square root of the right side: 77.459666924 Break this problem into two subproblems by setting (x + -50) equal to 77.459666924 and -77.459666924.Subproblem 1
x + -50 = 77.459666924 Simplifying x + -50 = 77.459666924 Reorder the terms: -50 + x = 77.459666924 Solving -50 + x = 77.459666924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 77.459666924 + 50 Combine like terms: -50 + 50 = 0 0 + x = 77.459666924 + 50 x = 77.459666924 + 50 Combine like terms: 77.459666924 + 50 = 127.459666924 x = 127.459666924 Simplifying x = 127.459666924Subproblem 2
x + -50 = -77.459666924 Simplifying x + -50 = -77.459666924 Reorder the terms: -50 + x = -77.459666924 Solving -50 + x = -77.459666924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -77.459666924 + 50 Combine like terms: -50 + 50 = 0 0 + x = -77.459666924 + 50 x = -77.459666924 + 50 Combine like terms: -77.459666924 + 50 = -27.459666924 x = -27.459666924 Simplifying x = -27.459666924Solution
The solution to the problem is based on the solutions from the subproblems. x = {127.459666924, -27.459666924}
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