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Simplifying -16x2 + -4x + 382 = 0 Reorder the terms: 382 + -4x + -16x2 = 0 Solving 382 + -4x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(191 + -2x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(191 + -2x + -8x2)' equal to zero and attempt to solve: Simplifying 191 + -2x + -8x2 = 0 Solving 191 + -2x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -23.875 + 0.25x + x2 = 0 Move the constant term to the right: Add '23.875' to each side of the equation. -23.875 + 0.25x + 23.875 + x2 = 0 + 23.875 Reorder the terms: -23.875 + 23.875 + 0.25x + x2 = 0 + 23.875 Combine like terms: -23.875 + 23.875 = 0.000 0.000 + 0.25x + x2 = 0 + 23.875 0.25x + x2 = 0 + 23.875 Combine like terms: 0 + 23.875 = 23.875 0.25x + x2 = 23.875 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 23.875 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 23.875 + 0.015625 Combine like terms: 23.875 + 0.015625 = 23.890625 0.015625 + 0.25x + x2 = 23.890625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 23.890625 Calculate the square root of the right side: 4.887803699 Break this problem into two subproblems by setting (x + 0.125) equal to 4.887803699 and -4.887803699.Subproblem 1
x + 0.125 = 4.887803699 Simplifying x + 0.125 = 4.887803699 Reorder the terms: 0.125 + x = 4.887803699 Solving 0.125 + x = 4.887803699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 4.887803699 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 4.887803699 + -0.125 x = 4.887803699 + -0.125 Combine like terms: 4.887803699 + -0.125 = 4.762803699 x = 4.762803699 Simplifying x = 4.762803699Subproblem 2
x + 0.125 = -4.887803699 Simplifying x + 0.125 = -4.887803699 Reorder the terms: 0.125 + x = -4.887803699 Solving 0.125 + x = -4.887803699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -4.887803699 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -4.887803699 + -0.125 x = -4.887803699 + -0.125 Combine like terms: -4.887803699 + -0.125 = -5.012803699 x = -5.012803699 Simplifying x = -5.012803699Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.762803699, -5.012803699}Solution
x = {4.762803699, -5.012803699}
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