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Simplifying 0 = -16x2 + 116x + 101 Reorder the terms: 0 = 101 + 116x + -16x2 Solving 0 = 101 + 116x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -101 = -101 -101 + -116x + 16x2 = 101 + 116x + -16x2 + -101 + -116x + 16x2 Reorder the terms: -101 + -116x + 16x2 = 101 + -101 + 116x + -116x + -16x2 + 16x2 Combine like terms: 101 + -101 = 0 -101 + -116x + 16x2 = 0 + 116x + -116x + -16x2 + 16x2 -101 + -116x + 16x2 = 116x + -116x + -16x2 + 16x2 Combine like terms: 116x + -116x = 0 -101 + -116x + 16x2 = 0 + -16x2 + 16x2 -101 + -116x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -101 + -116x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.3125 + -7.25x + x2 = 0 Move the constant term to the right: Add '6.3125' to each side of the equation. -6.3125 + -7.25x + 6.3125 + x2 = 0 + 6.3125 Reorder the terms: -6.3125 + 6.3125 + -7.25x + x2 = 0 + 6.3125 Combine like terms: -6.3125 + 6.3125 = 0.0000 0.0000 + -7.25x + x2 = 0 + 6.3125 -7.25x + x2 = 0 + 6.3125 Combine like terms: 0 + 6.3125 = 6.3125 -7.25x + x2 = 6.3125 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = 6.3125 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = 6.3125 + 13.140625 Combine like terms: 6.3125 + 13.140625 = 19.453125 13.140625 + -7.25x + x2 = 19.453125 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 19.453125 Calculate the square root of the right side: 4.410569691 Break this problem into two subproblems by setting (x + -3.625) equal to 4.410569691 and -4.410569691.Subproblem 1
x + -3.625 = 4.410569691 Simplifying x + -3.625 = 4.410569691 Reorder the terms: -3.625 + x = 4.410569691 Solving -3.625 + x = 4.410569691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 4.410569691 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 4.410569691 + 3.625 x = 4.410569691 + 3.625 Combine like terms: 4.410569691 + 3.625 = 8.035569691 x = 8.035569691 Simplifying x = 8.035569691Subproblem 2
x + -3.625 = -4.410569691 Simplifying x + -3.625 = -4.410569691 Reorder the terms: -3.625 + x = -4.410569691 Solving -3.625 + x = -4.410569691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -4.410569691 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -4.410569691 + 3.625 x = -4.410569691 + 3.625 Combine like terms: -4.410569691 + 3.625 = -0.785569691 x = -0.785569691 Simplifying x = -0.785569691Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.035569691, -0.785569691}
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