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Simplifying 0.25 = -0.5(32x2) + 20x + 3 Remove parenthesis around (32x2) 0.25 = -0.5 * 32x2 + 20x + 3 Multiply -0.5 * 32 0.25 = -16x2 + 20x + 3 Reorder the terms: 0.25 = 3 + 20x + -16x2 Solving 0.25 = 3 + 20x + -16x2 Solving for variable 'x'. Combine like terms: 0.25 + -3 = -2.75 -2.75 + -20x + 16x2 = 3 + 20x + -16x2 + -3 + -20x + 16x2 Reorder the terms: -2.75 + -20x + 16x2 = 3 + -3 + 20x + -20x + -16x2 + 16x2 Combine like terms: 3 + -3 = 0 -2.75 + -20x + 16x2 = 0 + 20x + -20x + -16x2 + 16x2 -2.75 + -20x + 16x2 = 20x + -20x + -16x2 + 16x2 Combine like terms: 20x + -20x = 0 -2.75 + -20x + 16x2 = 0 + -16x2 + 16x2 -2.75 + -20x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -2.75 + -20x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.171875 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.171875' to each side of the equation. -0.171875 + -1.25x + 0.171875 + x2 = 0 + 0.171875 Reorder the terms: -0.171875 + 0.171875 + -1.25x + x2 = 0 + 0.171875 Combine like terms: -0.171875 + 0.171875 = 0.000000 0.000000 + -1.25x + x2 = 0 + 0.171875 -1.25x + x2 = 0 + 0.171875 Combine like terms: 0 + 0.171875 = 0.171875 -1.25x + x2 = 0.171875 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 = 0.171875 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.171875 + 0.390625 Combine like terms: 0.171875 + 0.390625 = 0.5625 0.390625 + -1.25x + x2 = 0.5625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.5625 Calculate the square root of the right side: 0.75 Break this problem into two subproblems by setting (x + -0.625) equal to 0.75 and -0.75.Subproblem 1
x + -0.625 = 0.75 Simplifying x + -0.625 = 0.75 Reorder the terms: -0.625 + x = 0.75 Solving -0.625 + x = 0.75 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 = 0.75 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.75 + 0.625 x = 0.75 + 0.625 Combine like terms: 0.75 + 0.625 = 1.375 x = 1.375 Simplifying x = 1.375Subproblem 2
x + -0.625 = -0.75 Simplifying x + -0.625 = -0.75 Reorder the terms: -0.625 + x = -0.75 Solving -0.625 + x = -0.75 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 = -0.75 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.75 + 0.625 x = -0.75 + 0.625 Combine like terms: -0.75 + 0.625 = -0.125 x = -0.125 Simplifying x = -0.125Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.375, -0.125}
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