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Simplifying 8x2 + -16x + -46 = 0 Reorder the terms: -46 + -16x + 8x2 = 0 Solving -46 + -16x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + -8x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + -8x + 4x2)' equal to zero and attempt to solve: Simplifying -23 + -8x + 4x2 = 0 Solving -23 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.75 + -2x + x2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + -2x + 5.75 + x2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + -2x + x2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + -2x + x2 = 0 + 5.75 -2x + x2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 -2x + x2 = 5.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 5.75 + 1 Reorder the terms: 1 + -2x + x2 = 5.75 + 1 Combine like terms: 5.75 + 1 = 6.75 1 + -2x + x2 = 6.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + -1) equal to 2.598076211 and -2.598076211.Subproblem 1
x + -1 = 2.598076211 Simplifying x + -1 = 2.598076211 Reorder the terms: -1 + x = 2.598076211 Solving -1 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.598076211 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.598076211 + 1 x = 2.598076211 + 1 Combine like terms: 2.598076211 + 1 = 3.598076211 x = 3.598076211 Simplifying x = 3.598076211Subproblem 2
x + -1 = -2.598076211 Simplifying x + -1 = -2.598076211 Reorder the terms: -1 + x = -2.598076211 Solving -1 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.598076211 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.598076211 + 1 x = -2.598076211 + 1 Combine like terms: -2.598076211 + 1 = -1.598076211 x = -1.598076211 Simplifying x = -1.598076211Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.598076211, -1.598076211}Solution
x = {3.598076211, -1.598076211}
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