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Simplifying 0 = -16x2 + 16x + 3 Reorder the terms: 0 = 3 + 16x + -16x2 Solving 0 = 3 + 16x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -16x + 16x2 = 3 + 16x + -16x2 + -3 + -16x + 16x2 Reorder the terms: -3 + -16x + 16x2 = 3 + -3 + 16x + -16x + -16x2 + 16x2 Combine like terms: 3 + -3 = 0 -3 + -16x + 16x2 = 0 + 16x + -16x + -16x2 + 16x2 -3 + -16x + 16x2 = 16x + -16x + -16x2 + 16x2 Combine like terms: 16x + -16x = 0 -3 + -16x + 16x2 = 0 + -16x2 + 16x2 -3 + -16x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -3 + -16x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -1x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -1x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -1x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -1x + x2 = 0 + 0.1875 -1x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -1x + x2 = 0.1875 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.1875 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.1875 + 0.25 Combine like terms: 0.1875 + 0.25 = 0.4375 0.25 + -1x + x2 = 0.4375 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (x + -0.5) equal to 0.661437828 and -0.661437828.Subproblem 1
x + -0.5 = 0.661437828 Simplifying x + -0.5 = 0.661437828 Reorder the terms: -0.5 + x = 0.661437828 Solving -0.5 + x = 0.661437828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.661437828 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.661437828 + 0.5 x = 0.661437828 + 0.5 Combine like terms: 0.661437828 + 0.5 = 1.161437828 x = 1.161437828 Simplifying x = 1.161437828Subproblem 2
x + -0.5 = -0.661437828 Simplifying x + -0.5 = -0.661437828 Reorder the terms: -0.5 + x = -0.661437828 Solving -0.5 + x = -0.661437828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.661437828 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.661437828 + 0.5 x = -0.661437828 + 0.5 Combine like terms: -0.661437828 + 0.5 = -0.161437828 x = -0.161437828 Simplifying x = -0.161437828Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.161437828, -0.161437828}
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