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Simplifying (150 + -5x) = 0.002x2 + 1.5 Remove parenthesis around (150 + -5x) 150 + -5x = 0.002x2 + 1.5 Reorder the terms: 150 + -5x = 1.5 + 0.002x2 Solving 150 + -5x = 1.5 + 0.002x2 Solving for variable 'x'. Reorder the terms: 150 + -1.5 + -5x + -0.002x2 = 1.5 + 0.002x2 + -1.5 + -0.002x2 Combine like terms: 150 + -1.5 = 148.5 148.5 + -5x + -0.002x2 = 1.5 + 0.002x2 + -1.5 + -0.002x2 Reorder the terms: 148.5 + -5x + -0.002x2 = 1.5 + -1.5 + 0.002x2 + -0.002x2 Combine like terms: 1.5 + -1.5 = 0.0 148.5 + -5x + -0.002x2 = 0.0 + 0.002x2 + -0.002x2 148.5 + -5x + -0.002x2 = 0.002x2 + -0.002x2 Combine like terms: 0.002x2 + -0.002x2 = 0.000 148.5 + -5x + -0.002x2 = 0.000 Begin completing the square. Divide all terms by -0.002 the coefficient of the squared term: Divide each side by '-0.002'. -74250 + 2500x + x2 = 0 Move the constant term to the right: Add '74250' to each side of the equation. -74250 + 2500x + 74250 + x2 = 0 + 74250 Reorder the terms: -74250 + 74250 + 2500x + x2 = 0 + 74250 Combine like terms: -74250 + 74250 = 0 0 + 2500x + x2 = 0 + 74250 2500x + x2 = 0 + 74250 Combine like terms: 0 + 74250 = 74250 2500x + x2 = 74250 The x term is 2500x. Take half its coefficient (1250). Square it (1562500) and add it to both sides. Add '1562500' to each side of the equation. 2500x + 1562500 + x2 = 74250 + 1562500 Reorder the terms: 1562500 + 2500x + x2 = 74250 + 1562500 Combine like terms: 74250 + 1562500 = 1636750 1562500 + 2500x + x2 = 1636750 Factor a perfect square on the left side: (x + 1250)(x + 1250) = 1636750 Calculate the square root of the right side: 1279.355306395 Break this problem into two subproblems by setting (x + 1250) equal to 1279.355306395 and -1279.355306395.Subproblem 1
x + 1250 = 1279.355306395 Simplifying x + 1250 = 1279.355306395 Reorder the terms: 1250 + x = 1279.355306395 Solving 1250 + x = 1279.355306395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1250' to each side of the equation. 1250 + -1250 + x = 1279.355306395 + -1250 Combine like terms: 1250 + -1250 = 0 0 + x = 1279.355306395 + -1250 x = 1279.355306395 + -1250 Combine like terms: 1279.355306395 + -1250 = 29.355306395 x = 29.355306395 Simplifying x = 29.355306395Subproblem 2
x + 1250 = -1279.355306395 Simplifying x + 1250 = -1279.355306395 Reorder the terms: 1250 + x = -1279.355306395 Solving 1250 + x = -1279.355306395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1250' to each side of the equation. 1250 + -1250 + x = -1279.355306395 + -1250 Combine like terms: 1250 + -1250 = 0 0 + x = -1279.355306395 + -1250 x = -1279.355306395 + -1250 Combine like terms: -1279.355306395 + -1250 = -2529.355306395 x = -2529.355306395 Simplifying x = -2529.355306395Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.355306395, -2529.355306395}
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