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Simplifying 0 = -16x2 + 50x + 5 Reorder the terms: 0 = 5 + 50x + -16x2 Solving 0 = 5 + 50x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -50x + 16x2 = 5 + 50x + -16x2 + -5 + -50x + 16x2 Reorder the terms: -5 + -50x + 16x2 = 5 + -5 + 50x + -50x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 -5 + -50x + 16x2 = 0 + 50x + -50x + -16x2 + 16x2 -5 + -50x + 16x2 = 50x + -50x + -16x2 + 16x2 Combine like terms: 50x + -50x = 0 -5 + -50x + 16x2 = 0 + -16x2 + 16x2 -5 + -50x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -5 + -50x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -3.125x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -3.125x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -3.125x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -3.125x + x2 = 0 + 0.3125 -3.125x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -3.125x + x2 = 0.3125 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 0.3125 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 0.3125 + 2.44140625 Combine like terms: 0.3125 + 2.44140625 = 2.75390625 2.44140625 + -3.125x + x2 = 2.75390625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 2.75390625 Calculate the square root of the right side: 1.659489756 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.659489756 and -1.659489756.Subproblem 1
x + -1.5625 = 1.659489756 Simplifying x + -1.5625 = 1.659489756 Reorder the terms: -1.5625 + x = 1.659489756 Solving -1.5625 + x = 1.659489756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.659489756 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.659489756 + 1.5625 x = 1.659489756 + 1.5625 Combine like terms: 1.659489756 + 1.5625 = 3.221989756 x = 3.221989756 Simplifying x = 3.221989756Subproblem 2
x + -1.5625 = -1.659489756 Simplifying x + -1.5625 = -1.659489756 Reorder the terms: -1.5625 + x = -1.659489756 Solving -1.5625 + x = -1.659489756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.659489756 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.659489756 + 1.5625 x = -1.659489756 + 1.5625 Combine like terms: -1.659489756 + 1.5625 = -0.096989756 x = -0.096989756 Simplifying x = -0.096989756Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.221989756, -0.096989756}
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