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Simplifying -16x2 + -2x + 435 = 0 Reorder the terms: 435 + -2x + -16x2 = 0 Solving 435 + -2x + -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'. -27.1875 + 0.125x + x2 = 0 Move the constant term to the right: Add '27.1875' to each side of the equation. -27.1875 + 0.125x + 27.1875 + x2 = 0 + 27.1875 Reorder the terms: -27.1875 + 27.1875 + 0.125x + x2 = 0 + 27.1875 Combine like terms: -27.1875 + 27.1875 = 0.0000 0.0000 + 0.125x + x2 = 0 + 27.1875 0.125x + x2 = 0 + 27.1875 Combine like terms: 0 + 27.1875 = 27.1875 0.125x + x2 = 27.1875 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 27.1875 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 27.1875 + 0.00390625 Combine like terms: 27.1875 + 0.00390625 = 27.19140625 0.00390625 + 0.125x + x2 = 27.19140625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 27.19140625 Calculate the square root of the right side: 5.214537971 Break this problem into two subproblems by setting (x + 0.0625) equal to 5.214537971 and -5.214537971.Subproblem 1
x + 0.0625 = 5.214537971 Simplifying x + 0.0625 = 5.214537971 Reorder the terms: 0.0625 + x = 5.214537971 Solving 0.0625 + x = 5.214537971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 5.214537971 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 5.214537971 + -0.0625 x = 5.214537971 + -0.0625 Combine like terms: 5.214537971 + -0.0625 = 5.152037971 x = 5.152037971 Simplifying x = 5.152037971Subproblem 2
x + 0.0625 = -5.214537971 Simplifying x + 0.0625 = -5.214537971 Reorder the terms: 0.0625 + x = -5.214537971 Solving 0.0625 + x = -5.214537971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -5.214537971 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -5.214537971 + -0.0625 x = -5.214537971 + -0.0625 Combine like terms: -5.214537971 + -0.0625 = -5.277037971 x = -5.277037971 Simplifying x = -5.277037971Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.152037971, -5.277037971}
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