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Simplifying -16x2 + 31x + 6 = 0 Reorder the terms: 6 + 31x + -16x2 = 0 Solving 6 + 31x + -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'. -0.375 + -1.9375x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -1.9375x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -1.9375x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -1.9375x + x2 = 0 + 0.375 -1.9375x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -1.9375x + x2 = 0.375 The x term is -1.9375x. Take half its coefficient (-0.96875). Square it (0.9384765625) and add it to both sides. Add '0.9384765625' to each side of the equation. -1.9375x + 0.9384765625 + x2 = 0.375 + 0.9384765625 Reorder the terms: 0.9384765625 + -1.9375x + x2 = 0.375 + 0.9384765625 Combine like terms: 0.375 + 0.9384765625 = 1.3134765625 0.9384765625 + -1.9375x + x2 = 1.3134765625 Factor a perfect square on the left side: (x + -0.96875)(x + -0.96875) = 1.3134765625 Calculate the square root of the right side: 1.146070051 Break this problem into two subproblems by setting (x + -0.96875) equal to 1.146070051 and -1.146070051.Subproblem 1
x + -0.96875 = 1.146070051 Simplifying x + -0.96875 = 1.146070051 Reorder the terms: -0.96875 + x = 1.146070051 Solving -0.96875 + x = 1.146070051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + x = 1.146070051 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = 1.146070051 + 0.96875 x = 1.146070051 + 0.96875 Combine like terms: 1.146070051 + 0.96875 = 2.114820051 x = 2.114820051 Simplifying x = 2.114820051Subproblem 2
x + -0.96875 = -1.146070051 Simplifying x + -0.96875 = -1.146070051 Reorder the terms: -0.96875 + x = -1.146070051 Solving -0.96875 + x = -1.146070051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + x = -1.146070051 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = -1.146070051 + 0.96875 x = -1.146070051 + 0.96875 Combine like terms: -1.146070051 + 0.96875 = -0.177320051 x = -0.177320051 Simplifying x = -0.177320051Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.114820051, -0.177320051}
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