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Simplifying 9.2 = -0.01x2 + 0.24x + 8.76 Reorder the terms: 9.2 = 8.76 + 0.24x + -0.01x2 Solving 9.2 = 8.76 + 0.24x + -0.01x2 Solving for variable 'x'. Combine like terms: 9.2 + -8.76 = 0.44 0.44 + -0.24x + 0.01x2 = 8.76 + 0.24x + -0.01x2 + -8.76 + -0.24x + 0.01x2 Reorder the terms: 0.44 + -0.24x + 0.01x2 = 8.76 + -8.76 + 0.24x + -0.24x + -0.01x2 + 0.01x2 Combine like terms: 8.76 + -8.76 = 0.00 0.44 + -0.24x + 0.01x2 = 0.00 + 0.24x + -0.24x + -0.01x2 + 0.01x2 0.44 + -0.24x + 0.01x2 = 0.24x + -0.24x + -0.01x2 + 0.01x2 Combine like terms: 0.24x + -0.24x = 0.00 0.44 + -0.24x + 0.01x2 = 0.00 + -0.01x2 + 0.01x2 0.44 + -0.24x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 0.44 + -0.24x + 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'. 44 + -24x + x2 = 0 Move the constant term to the right: Add '-44' to each side of the equation. 44 + -24x + -44 + x2 = 0 + -44 Reorder the terms: 44 + -44 + -24x + x2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -24x + x2 = 0 + -44 -24x + x2 = 0 + -44 Combine like terms: 0 + -44 = -44 -24x + x2 = -44 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -44 + 144 Reorder the terms: 144 + -24x + x2 = -44 + 144 Combine like terms: -44 + 144 = 100 144 + -24x + x2 = 100 Factor a perfect square on the left side: (x + -12)(x + -12) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + -12) equal to 10 and -10.Subproblem 1
x + -12 = 10 Simplifying x + -12 = 10 Reorder the terms: -12 + x = 10 Solving -12 + x = 10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 10 + 12 Combine like terms: -12 + 12 = 0 0 + x = 10 + 12 x = 10 + 12 Combine like terms: 10 + 12 = 22 x = 22 Simplifying x = 22Subproblem 2
x + -12 = -10 Simplifying x + -12 = -10 Reorder the terms: -12 + x = -10 Solving -12 + x = -10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -10 + 12 Combine like terms: -12 + 12 = 0 0 + x = -10 + 12 x = -10 + 12 Combine like terms: -10 + 12 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {22, 2}
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