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Simplifying 9.3 = -0.01x2 + 0.29x + 8.1 Reorder the terms: 9.3 = 8.1 + 0.29x + -0.01x2 Solving 9.3 = 8.1 + 0.29x + -0.01x2 Solving for variable 'x'. Combine like terms: 9.3 + -8.1 = 1.2 1.2 + -0.29x + 0.01x2 = 8.1 + 0.29x + -0.01x2 + -8.1 + -0.29x + 0.01x2 Reorder the terms: 1.2 + -0.29x + 0.01x2 = 8.1 + -8.1 + 0.29x + -0.29x + -0.01x2 + 0.01x2 Combine like terms: 8.1 + -8.1 = 0.0 1.2 + -0.29x + 0.01x2 = 0.0 + 0.29x + -0.29x + -0.01x2 + 0.01x2 1.2 + -0.29x + 0.01x2 = 0.29x + -0.29x + -0.01x2 + 0.01x2 Combine like terms: 0.29x + -0.29x = 0.00 1.2 + -0.29x + 0.01x2 = 0.00 + -0.01x2 + 0.01x2 1.2 + -0.29x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 1.2 + -0.29x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 120 + -29x + x2 = 0 Move the constant term to the right: Add '-120' to each side of the equation. 120 + -29x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + -29x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -29x + x2 = 0 + -120 -29x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 -29x + x2 = -120 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -120 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -120 + 210.25 Combine like terms: -120 + 210.25 = 90.25 210.25 + -29x + x2 = 90.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 90.25 Calculate the square root of the right side: 9.5 Break this problem into two subproblems by setting (x + -14.5) equal to 9.5 and -9.5.Subproblem 1
x + -14.5 = 9.5 Simplifying x + -14.5 = 9.5 Reorder the terms: -14.5 + x = 9.5 Solving -14.5 + x = 9.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 9.5 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 9.5 + 14.5 x = 9.5 + 14.5 Combine like terms: 9.5 + 14.5 = 24 x = 24 Simplifying x = 24Subproblem 2
x + -14.5 = -9.5 Simplifying x + -14.5 = -9.5 Reorder the terms: -14.5 + x = -9.5 Solving -14.5 + x = -9.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -9.5 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -9.5 + 14.5 x = -9.5 + 14.5 Combine like terms: -9.5 + 14.5 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {24, 5}
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