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Simplifying 8x2 + 26x + -96 = 0 Reorder the terms: -96 + 26x + 8x2 = 0 Solving -96 + 26x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-48 + 13x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-48 + 13x + 4x2)' equal to zero and attempt to solve: Simplifying -48 + 13x + 4x2 = 0 Solving -48 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12 + 3.25x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 3.25x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 3.25x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 3.25x + x2 = 0 + 12 3.25x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 3.25x + x2 = 12 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 12 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 12 + 2.640625 Combine like terms: 12 + 2.640625 = 14.640625 2.640625 + 3.25x + x2 = 14.640625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 14.640625 Calculate the square root of the right side: 3.826306966 Break this problem into two subproblems by setting (x + 1.625) equal to 3.826306966 and -3.826306966.Subproblem 1
x + 1.625 = 3.826306966 Simplifying x + 1.625 = 3.826306966 Reorder the terms: 1.625 + x = 3.826306966 Solving 1.625 + x = 3.826306966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 3.826306966 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 3.826306966 + -1.625 x = 3.826306966 + -1.625 Combine like terms: 3.826306966 + -1.625 = 2.201306966 x = 2.201306966 Simplifying x = 2.201306966Subproblem 2
x + 1.625 = -3.826306966 Simplifying x + 1.625 = -3.826306966 Reorder the terms: 1.625 + x = -3.826306966 Solving 1.625 + x = -3.826306966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -3.826306966 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -3.826306966 + -1.625 x = -3.826306966 + -1.625 Combine like terms: -3.826306966 + -1.625 = -5.451306966 x = -5.451306966 Simplifying x = -5.451306966Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.201306966, -5.451306966}Solution
x = {2.201306966, -5.451306966}
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