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Simplifying 3 = -16x2 + 20x + 6 Reorder the terms: 3 = 6 + 20x + -16x2 Solving 3 = 6 + 20x + -16x2 Solving for variable 'x'. Combine like terms: 3 + -6 = -3 -3 + -20x + 16x2 = 6 + 20x + -16x2 + -6 + -20x + 16x2 Reorder the terms: -3 + -20x + 16x2 = 6 + -6 + 20x + -20x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -3 + -20x + 16x2 = 0 + 20x + -20x + -16x2 + 16x2 -3 + -20x + 16x2 = 20x + -20x + -16x2 + 16x2 Combine like terms: 20x + -20x = 0 -3 + -20x + 16x2 = 0 + -16x2 + 16x2 -3 + -20x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -3 + -20x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -1.25x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -1.25x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -1.25x + x2 = 0 + 0.1875 -1.25x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -1.25x + x2 = 0.1875 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 = 0.1875 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.1875 + 0.390625 Combine like terms: 0.1875 + 0.390625 = 0.578125 0.390625 + -1.25x + x2 = 0.578125 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.578125 Calculate the square root of the right side: 0.760345316 Break this problem into two subproblems by setting (x + -0.625) equal to 0.760345316 and -0.760345316.Subproblem 1
x + -0.625 = 0.760345316 Simplifying x + -0.625 = 0.760345316 Reorder the terms: -0.625 + x = 0.760345316 Solving -0.625 + x = 0.760345316 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 = 0.760345316 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.760345316 + 0.625 x = 0.760345316 + 0.625 Combine like terms: 0.760345316 + 0.625 = 1.385345316 x = 1.385345316 Simplifying x = 1.385345316Subproblem 2
x + -0.625 = -0.760345316 Simplifying x + -0.625 = -0.760345316 Reorder the terms: -0.625 + x = -0.760345316 Solving -0.625 + x = -0.760345316 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 = -0.760345316 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.760345316 + 0.625 x = -0.760345316 + 0.625 Combine like terms: -0.760345316 + 0.625 = -0.135345316 x = -0.135345316 Simplifying x = -0.135345316Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.385345316, -0.135345316}
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