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Simplifying 9.8 = -0.01x2 + 0.28x + 8.65 Reorder the terms: 9.8 = 8.65 + 0.28x + -0.01x2 Solving 9.8 = 8.65 + 0.28x + -0.01x2 Solving for variable 'x'. Combine like terms: 9.8 + -8.65 = 1.15 1.15 + -0.28x + 0.01x2 = 8.65 + 0.28x + -0.01x2 + -8.65 + -0.28x + 0.01x2 Reorder the terms: 1.15 + -0.28x + 0.01x2 = 8.65 + -8.65 + 0.28x + -0.28x + -0.01x2 + 0.01x2 Combine like terms: 8.65 + -8.65 = 0.00 1.15 + -0.28x + 0.01x2 = 0.00 + 0.28x + -0.28x + -0.01x2 + 0.01x2 1.15 + -0.28x + 0.01x2 = 0.28x + -0.28x + -0.01x2 + 0.01x2 Combine like terms: 0.28x + -0.28x = 0.00 1.15 + -0.28x + 0.01x2 = 0.00 + -0.01x2 + 0.01x2 1.15 + -0.28x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 1.15 + -0.28x + 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'. 115 + -28x + x2 = 0 Move the constant term to the right: Add '-115' to each side of the equation. 115 + -28x + -115 + x2 = 0 + -115 Reorder the terms: 115 + -115 + -28x + x2 = 0 + -115 Combine like terms: 115 + -115 = 0 0 + -28x + x2 = 0 + -115 -28x + x2 = 0 + -115 Combine like terms: 0 + -115 = -115 -28x + x2 = -115 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -115 + 196 Reorder the terms: 196 + -28x + x2 = -115 + 196 Combine like terms: -115 + 196 = 81 196 + -28x + x2 = 81 Factor a perfect square on the left side: (x + -14)(x + -14) = 81 Calculate the square root of the right side: 9 Break this problem into two subproblems by setting (x + -14) equal to 9 and -9.Subproblem 1
x + -14 = 9 Simplifying x + -14 = 9 Reorder the terms: -14 + x = 9 Solving -14 + x = 9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 9 + 14 Combine like terms: -14 + 14 = 0 0 + x = 9 + 14 x = 9 + 14 Combine like terms: 9 + 14 = 23 x = 23 Simplifying x = 23Subproblem 2
x + -14 = -9 Simplifying x + -14 = -9 Reorder the terms: -14 + x = -9 Solving -14 + x = -9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -9 + 14 Combine like terms: -14 + 14 = 0 0 + x = -9 + 14 x = -9 + 14 Combine like terms: -9 + 14 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {23, 5}
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