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Simplifying 0 = -16x2 + 20x + 5 Reorder the terms: 0 = 5 + 20x + -16x2 Solving 0 = 5 + 20x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -20x + 16x2 = 5 + 20x + -16x2 + -5 + -20x + 16x2 Reorder the terms: -5 + -20x + 16x2 = 5 + -5 + 20x + -20x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 -5 + -20x + 16x2 = 0 + 20x + -20x + -16x2 + 16x2 -5 + -20x + 16x2 = 20x + -20x + -16x2 + 16x2 Combine like terms: 20x + -20x = 0 -5 + -20x + 16x2 = 0 + -16x2 + 16x2 -5 + -20x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -5 + -20x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -1.25x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -1.25x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -1.25x + x2 = 0 + 0.3125 -1.25x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -1.25x + x2 = 0.3125 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 = 0.3125 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.3125 + 0.390625 Combine like terms: 0.3125 + 0.390625 = 0.703125 0.390625 + -1.25x + x2 = 0.703125 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.703125 Calculate the square root of the right side: 0.838525492 Break this problem into two subproblems by setting (x + -0.625) equal to 0.838525492 and -0.838525492.Subproblem 1
x + -0.625 = 0.838525492 Simplifying x + -0.625 = 0.838525492 Reorder the terms: -0.625 + x = 0.838525492 Solving -0.625 + x = 0.838525492 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 = 0.838525492 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.838525492 + 0.625 x = 0.838525492 + 0.625 Combine like terms: 0.838525492 + 0.625 = 1.463525492 x = 1.463525492 Simplifying x = 1.463525492Subproblem 2
x + -0.625 = -0.838525492 Simplifying x + -0.625 = -0.838525492 Reorder the terms: -0.625 + x = -0.838525492 Solving -0.625 + x = -0.838525492 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 = -0.838525492 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.838525492 + 0.625 x = -0.838525492 + 0.625 Combine like terms: -0.838525492 + 0.625 = -0.213525492 x = -0.213525492 Simplifying x = -0.213525492Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.463525492, -0.213525492}
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