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Simplifying 0 = 0.06x2 + 1.2x + -150 Reorder the terms: 0 = -150 + 1.2x + 0.06x2 Solving 0 = -150 + 1.2x + 0.06x2 Solving for variable 'x'. Combine like terms: 0 + 150 = 150 150 + -1.2x + -0.06x2 = -150 + 1.2x + 0.06x2 + 150 + -1.2x + -0.06x2 Reorder the terms: 150 + -1.2x + -0.06x2 = -150 + 150 + 1.2x + -1.2x + 0.06x2 + -0.06x2 Combine like terms: -150 + 150 = 0 150 + -1.2x + -0.06x2 = 0 + 1.2x + -1.2x + 0.06x2 + -0.06x2 150 + -1.2x + -0.06x2 = 1.2x + -1.2x + 0.06x2 + -0.06x2 Combine like terms: 1.2x + -1.2x = 0.0 150 + -1.2x + -0.06x2 = 0.0 + 0.06x2 + -0.06x2 150 + -1.2x + -0.06x2 = 0.06x2 + -0.06x2 Combine like terms: 0.06x2 + -0.06x2 = 0.00 150 + -1.2x + -0.06x2 = 0.00 Begin completing the square. Divide all terms by -0.06 the coefficient of the squared term: Divide each side by '-0.06'. -2500 + 20x + x2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 20x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 20x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 20x + x2 = 0 + 2500 20x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 20x + x2 = 2500 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 2500 + 100 Reorder the terms: 100 + 20x + x2 = 2500 + 100 Combine like terms: 2500 + 100 = 2600 100 + 20x + x2 = 2600 Factor a perfect square on the left side: (x + 10)(x + 10) = 2600 Calculate the square root of the right side: 50.990195136 Break this problem into two subproblems by setting (x + 10) equal to 50.990195136 and -50.990195136.Subproblem 1
x + 10 = 50.990195136 Simplifying x + 10 = 50.990195136 Reorder the terms: 10 + x = 50.990195136 Solving 10 + x = 50.990195136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 50.990195136 + -10 Combine like terms: 10 + -10 = 0 0 + x = 50.990195136 + -10 x = 50.990195136 + -10 Combine like terms: 50.990195136 + -10 = 40.990195136 x = 40.990195136 Simplifying x = 40.990195136Subproblem 2
x + 10 = -50.990195136 Simplifying x + 10 = -50.990195136 Reorder the terms: 10 + x = -50.990195136 Solving 10 + x = -50.990195136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -50.990195136 + -10 Combine like terms: 10 + -10 = 0 0 + x = -50.990195136 + -10 x = -50.990195136 + -10 Combine like terms: -50.990195136 + -10 = -60.990195136 x = -60.990195136 Simplifying x = -60.990195136Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.990195136, -60.990195136}
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