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Simplifying 0 = 0.15x + -0.005x2 + -0.5 Reorder the terms: 0 = -0.5 + 0.15x + -0.005x2 Solving 0 = -0.5 + 0.15x + -0.005x2 Solving for variable 'x'. Combine like terms: 0 + 0.5 = 0.5 0.5 + -0.15x + 0.005x2 = -0.5 + 0.15x + -0.005x2 + 0.5 + -0.15x + 0.005x2 Reorder the terms: 0.5 + -0.15x + 0.005x2 = -0.5 + 0.5 + 0.15x + -0.15x + -0.005x2 + 0.005x2 Combine like terms: -0.5 + 0.5 = 0.0 0.5 + -0.15x + 0.005x2 = 0.0 + 0.15x + -0.15x + -0.005x2 + 0.005x2 0.5 + -0.15x + 0.005x2 = 0.15x + -0.15x + -0.005x2 + 0.005x2 Combine like terms: 0.15x + -0.15x = 0.00 0.5 + -0.15x + 0.005x2 = 0.00 + -0.005x2 + 0.005x2 0.5 + -0.15x + 0.005x2 = -0.005x2 + 0.005x2 Combine like terms: -0.005x2 + 0.005x2 = 0.000 0.5 + -0.15x + 0.005x2 = 0.000 Begin completing the square. Divide all terms by 0.005 the coefficient of the squared term: Divide each side by '0.005'. 100 + -30x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -30x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -30x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -30x + x2 = 0 + -100 -30x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -30x + x2 = -100 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -100 + 225 Reorder the terms: 225 + -30x + x2 = -100 + 225 Combine like terms: -100 + 225 = 125 225 + -30x + x2 = 125 Factor a perfect square on the left side: (x + -15)(x + -15) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + -15) equal to 11.180339887 and -11.180339887.Subproblem 1
x + -15 = 11.180339887 Simplifying x + -15 = 11.180339887 Reorder the terms: -15 + x = 11.180339887 Solving -15 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 11.180339887 + 15 Combine like terms: -15 + 15 = 0 0 + x = 11.180339887 + 15 x = 11.180339887 + 15 Combine like terms: 11.180339887 + 15 = 26.180339887 x = 26.180339887 Simplifying x = 26.180339887Subproblem 2
x + -15 = -11.180339887 Simplifying x + -15 = -11.180339887 Reorder the terms: -15 + x = -11.180339887 Solving -15 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -11.180339887 + 15 Combine like terms: -15 + 15 = 0 0 + x = -11.180339887 + 15 x = -11.180339887 + 15 Combine like terms: -11.180339887 + 15 = 3.819660113 x = 3.819660113 Simplifying x = 3.819660113Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.180339887, 3.819660113}
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