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Simplifying 150 + -0.5x = 0.002x2 + 1.5 Reorder the terms: 150 + -0.5x = 1.5 + 0.002x2 Solving 150 + -0.5x = 1.5 + 0.002x2 Solving for variable 'x'. Reorder the terms: 150 + -1.5 + -0.5x + -0.002x2 = 1.5 + 0.002x2 + -1.5 + -0.002x2 Combine like terms: 150 + -1.5 = 148.5 148.5 + -0.5x + -0.002x2 = 1.5 + 0.002x2 + -1.5 + -0.002x2 Reorder the terms: 148.5 + -0.5x + -0.002x2 = 1.5 + -1.5 + 0.002x2 + -0.002x2 Combine like terms: 1.5 + -1.5 = 0.0 148.5 + -0.5x + -0.002x2 = 0.0 + 0.002x2 + -0.002x2 148.5 + -0.5x + -0.002x2 = 0.002x2 + -0.002x2 Combine like terms: 0.002x2 + -0.002x2 = 0.000 148.5 + -0.5x + -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 + 250x + x2 = 0 Move the constant term to the right: Add '74250' to each side of the equation. -74250 + 250x + 74250 + x2 = 0 + 74250 Reorder the terms: -74250 + 74250 + 250x + x2 = 0 + 74250 Combine like terms: -74250 + 74250 = 0 0 + 250x + x2 = 0 + 74250 250x + x2 = 0 + 74250 Combine like terms: 0 + 74250 = 74250 250x + x2 = 74250 The x term is 250x. Take half its coefficient (125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. 250x + 15625 + x2 = 74250 + 15625 Reorder the terms: 15625 + 250x + x2 = 74250 + 15625 Combine like terms: 74250 + 15625 = 89875 15625 + 250x + x2 = 89875 Factor a perfect square on the left side: (x + 125)(x + 125) = 89875 Calculate the square root of the right side: 299.791594278 Break this problem into two subproblems by setting (x + 125) equal to 299.791594278 and -299.791594278.Subproblem 1
x + 125 = 299.791594278 Simplifying x + 125 = 299.791594278 Reorder the terms: 125 + x = 299.791594278 Solving 125 + x = 299.791594278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + x = 299.791594278 + -125 Combine like terms: 125 + -125 = 0 0 + x = 299.791594278 + -125 x = 299.791594278 + -125 Combine like terms: 299.791594278 + -125 = 174.791594278 x = 174.791594278 Simplifying x = 174.791594278Subproblem 2
x + 125 = -299.791594278 Simplifying x + 125 = -299.791594278 Reorder the terms: 125 + x = -299.791594278 Solving 125 + x = -299.791594278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + x = -299.791594278 + -125 Combine like terms: 125 + -125 = 0 0 + x = -299.791594278 + -125 x = -299.791594278 + -125 Combine like terms: -299.791594278 + -125 = -424.791594278 x = -424.791594278 Simplifying x = -424.791594278Solution
The solution to the problem is based on the solutions from the subproblems. x = {174.791594278, -424.791594278}
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