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Simplifying -0.5 * 32x2 + 20x + 3 = 9.25 Multiply -0.5 * 32 -16x2 + 20x + 3 = 9.25 Reorder the terms: 3 + 20x + -16x2 = 9.25 Solving 3 + 20x + -16x2 = 9.25 Solving for variable 'x'. Reorder the terms: 3 + -9.25 + 20x + -16x2 = 9.25 + -9.25 Combine like terms: 3 + -9.25 = -6.25 -6.25 + 20x + -16x2 = 9.25 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 -6.25 + 20x + -16x2 = 0.00 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.390625 + -1.25x + x2 = 0.00 Move the constant term to the right: Add '-0.390625' to each side of the equation. 0.390625 + -1.25x + -0.390625 + x2 = 0.00 + -0.390625 Reorder the terms: 0.390625 + -0.390625 + -1.25x + x2 = 0.00 + -0.390625 Combine like terms: 0.390625 + -0.390625 = 0.000000 0.000000 + -1.25x + x2 = 0.00 + -0.390625 -1.25x + x2 = 0.00 + -0.390625 Combine like terms: 0.00 + -0.390625 = -0.390625 -1.25x + x2 = -0.390625 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.390625 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.390625 + 0.390625 Combine like terms: -0.390625 + 0.390625 = 0.000000 0.390625 + -1.25x + x2 = 0.000000 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.000000 Calculate the square root of the right side: 0.000000 Break this problem into two subproblems by setting (x + -0.625) equal to 0.000000 and 0.000000.Subproblem 1
x + -0.625 = 0.000000 Simplifying x + -0.625 = 0.000000 Reorder the terms: -0.625 + x = 0.000000 Solving -0.625 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.000000 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.000000 + 0.625 x = 0.000000 + 0.625 Combine like terms: 0.000000 + 0.625 = 0.625 x = 0.625 Simplifying x = 0.625Subproblem 2
x + -0.625 = 0.000000 Simplifying x + -0.625 = 0.000000 Reorder the terms: -0.625 + x = 0.000000 Solving -0.625 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.000000 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.000000 + 0.625 x = 0.000000 + 0.625 Combine like terms: 0.000000 + 0.625 = 0.625 x = 0.625 Simplifying x = 0.625Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.625, 0.625}
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