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Simplifying 9.3 = -0.01x2 + 0.25x + 8.84 Reorder the terms: 9.3 = 8.84 + 0.25x + -0.01x2 Solving 9.3 = 8.84 + 0.25x + -0.01x2 Solving for variable 'x'. Combine like terms: 9.3 + -8.84 = 0.46 0.46 + -0.25x + 0.01x2 = 8.84 + 0.25x + -0.01x2 + -8.84 + -0.25x + 0.01x2 Reorder the terms: 0.46 + -0.25x + 0.01x2 = 8.84 + -8.84 + 0.25x + -0.25x + -0.01x2 + 0.01x2 Combine like terms: 8.84 + -8.84 = 0.00 0.46 + -0.25x + 0.01x2 = 0.00 + 0.25x + -0.25x + -0.01x2 + 0.01x2 0.46 + -0.25x + 0.01x2 = 0.25x + -0.25x + -0.01x2 + 0.01x2 Combine like terms: 0.25x + -0.25x = 0.00 0.46 + -0.25x + 0.01x2 = 0.00 + -0.01x2 + 0.01x2 0.46 + -0.25x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 0.46 + -0.25x + 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'. 46 + -25x + x2 = 0 Move the constant term to the right: Add '-46' to each side of the equation. 46 + -25x + -46 + x2 = 0 + -46 Reorder the terms: 46 + -46 + -25x + x2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -25x + x2 = 0 + -46 -25x + x2 = 0 + -46 Combine like terms: 0 + -46 = -46 -25x + x2 = -46 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -46 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -46 + 156.25 Combine like terms: -46 + 156.25 = 110.25 156.25 + -25x + x2 = 110.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 110.25 Calculate the square root of the right side: 10.5 Break this problem into two subproblems by setting (x + -12.5) equal to 10.5 and -10.5.Subproblem 1
x + -12.5 = 10.5 Simplifying x + -12.5 = 10.5 Reorder the terms: -12.5 + x = 10.5 Solving -12.5 + x = 10.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 10.5 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 10.5 + 12.5 x = 10.5 + 12.5 Combine like terms: 10.5 + 12.5 = 23 x = 23 Simplifying x = 23Subproblem 2
x + -12.5 = -10.5 Simplifying x + -12.5 = -10.5 Reorder the terms: -12.5 + x = -10.5 Solving -12.5 + x = -10.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -10.5 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -10.5 + 12.5 x = -10.5 + 12.5 Combine like terms: -10.5 + 12.5 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {23, 2}
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