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Simplifying 16x2 + 50x + 5 = 0 Reorder the terms: 5 + 50x + 16x2 = 0 Solving 5 + 50x + 16x2 = 0 Solving for variable 'x'. 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 = 2.12890625 2.44140625 + 3.125x + x2 = 2.12890625 Factor a perfect square on the left side: (x + 1.5625)(x + 1.5625) = 2.12890625 Calculate the square root of the right side: 1.459077191 Break this problem into two subproblems by setting (x + 1.5625) equal to 1.459077191 and -1.459077191.Subproblem 1
x + 1.5625 = 1.459077191 Simplifying x + 1.5625 = 1.459077191 Reorder the terms: 1.5625 + x = 1.459077191 Solving 1.5625 + x = 1.459077191 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 = 1.459077191 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 1.459077191 + -1.5625 x = 1.459077191 + -1.5625 Combine like terms: 1.459077191 + -1.5625 = -0.103422809 x = -0.103422809 Simplifying x = -0.103422809Subproblem 2
x + 1.5625 = -1.459077191 Simplifying x + 1.5625 = -1.459077191 Reorder the terms: 1.5625 + x = -1.459077191 Solving 1.5625 + x = -1.459077191 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 = -1.459077191 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -1.459077191 + -1.5625 x = -1.459077191 + -1.5625 Combine like terms: -1.459077191 + -1.5625 = -3.021577191 x = -3.021577191 Simplifying x = -3.021577191Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.103422809, -3.021577191}
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