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Simplifying 16x2 + -8x + -26 = 0 Reorder the terms: -26 + -8x + 16x2 = 0 Solving -26 + -8x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -4x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -4x + 8x2)' equal to zero and attempt to solve: Simplifying -13 + -4x + 8x2 = 0 Solving -13 + -4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + -0.5x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + -0.5x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + -0.5x + x2 = 0 + 1.625 -0.5x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 -0.5x + x2 = 1.625 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.625 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.625 + 0.0625 Combine like terms: 1.625 + 0.0625 = 1.6875 0.0625 + -0.5x + x2 = 1.6875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.6875 Calculate the square root of the right side: 1.299038106 Break this problem into two subproblems by setting (x + -0.25) equal to 1.299038106 and -1.299038106.Subproblem 1
x + -0.25 = 1.299038106 Simplifying x + -0.25 = 1.299038106 Reorder the terms: -0.25 + x = 1.299038106 Solving -0.25 + x = 1.299038106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.299038106 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.299038106 + 0.25 x = 1.299038106 + 0.25 Combine like terms: 1.299038106 + 0.25 = 1.549038106 x = 1.549038106 Simplifying x = 1.549038106Subproblem 2
x + -0.25 = -1.299038106 Simplifying x + -0.25 = -1.299038106 Reorder the terms: -0.25 + x = -1.299038106 Solving -0.25 + x = -1.299038106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.299038106 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.299038106 + 0.25 x = -1.299038106 + 0.25 Combine like terms: -1.299038106 + 0.25 = -1.049038106 x = -1.049038106 Simplifying x = -1.049038106Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.549038106, -1.049038106}Solution
x = {1.549038106, -1.049038106}
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