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Simplifying 228 = -0.64x2 + 24x + 3 Reorder the terms: 228 = 3 + 24x + -0.64x2 Solving 228 = 3 + 24x + -0.64x2 Solving for variable 'x'. Combine like terms: 228 + -3 = 225 225 + -24x + 0.64x2 = 3 + 24x + -0.64x2 + -3 + -24x + 0.64x2 Reorder the terms: 225 + -24x + 0.64x2 = 3 + -3 + 24x + -24x + -0.64x2 + 0.64x2 Combine like terms: 3 + -3 = 0 225 + -24x + 0.64x2 = 0 + 24x + -24x + -0.64x2 + 0.64x2 225 + -24x + 0.64x2 = 24x + -24x + -0.64x2 + 0.64x2 Combine like terms: 24x + -24x = 0 225 + -24x + 0.64x2 = 0 + -0.64x2 + 0.64x2 225 + -24x + 0.64x2 = -0.64x2 + 0.64x2 Combine like terms: -0.64x2 + 0.64x2 = 0.00 225 + -24x + 0.64x2 = 0.00 Begin completing the square. Divide all terms by 0.64 the coefficient of the squared term: Divide each side by '0.64'. 351.5625 + -37.5x + x2 = 0 Move the constant term to the right: Add '-351.5625' to each side of the equation. 351.5625 + -37.5x + -351.5625 + x2 = 0 + -351.5625 Reorder the terms: 351.5625 + -351.5625 + -37.5x + x2 = 0 + -351.5625 Combine like terms: 351.5625 + -351.5625 = 0.0000 0.0000 + -37.5x + x2 = 0 + -351.5625 -37.5x + x2 = 0 + -351.5625 Combine like terms: 0 + -351.5625 = -351.5625 -37.5x + x2 = -351.5625 The x term is -37.5x. Take half its coefficient (-18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. -37.5x + 351.5625 + x2 = -351.5625 + 351.5625 Reorder the terms: 351.5625 + -37.5x + x2 = -351.5625 + 351.5625 Combine like terms: -351.5625 + 351.5625 = 0.0000 351.5625 + -37.5x + x2 = 0.0000 Factor a perfect square on the left side: (x + -18.75)(x + -18.75) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + -18.75) equal to 0.0000 and 0.0000.Subproblem 1
x + -18.75 = 0.0000 Simplifying x + -18.75 = 0.0000 Reorder the terms: -18.75 + x = 0.0000 Solving -18.75 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = 0.0000 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = 0.0000 + 18.75 x = 0.0000 + 18.75 Combine like terms: 0.0000 + 18.75 = 18.75 x = 18.75 Simplifying x = 18.75Subproblem 2
x + -18.75 = 0.0000 Simplifying x + -18.75 = 0.0000 Reorder the terms: -18.75 + x = 0.0000 Solving -18.75 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = 0.0000 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = 0.0000 + 18.75 x = 0.0000 + 18.75 Combine like terms: 0.0000 + 18.75 = 18.75 x = 18.75 Simplifying x = 18.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.75, 18.75}
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