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Simplifying 8x2 + 26x + 20 = 386 Reorder the terms: 20 + 26x + 8x2 = 386 Solving 20 + 26x + 8x2 = 386 Solving for variable 'x'. Reorder the terms: 20 + -386 + 26x + 8x2 = 386 + -386 Combine like terms: 20 + -386 = -366 -366 + 26x + 8x2 = 386 + -386 Combine like terms: 386 + -386 = 0 -366 + 26x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-183 + 13x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-183 + 13x + 4x2)' equal to zero and attempt to solve: Simplifying -183 + 13x + 4x2 = 0 Solving -183 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -45.75 + 3.25x + x2 = 0 Move the constant term to the right: Add '45.75' to each side of the equation. -45.75 + 3.25x + 45.75 + x2 = 0 + 45.75 Reorder the terms: -45.75 + 45.75 + 3.25x + x2 = 0 + 45.75 Combine like terms: -45.75 + 45.75 = 0.00 0.00 + 3.25x + x2 = 0 + 45.75 3.25x + x2 = 0 + 45.75 Combine like terms: 0 + 45.75 = 45.75 3.25x + x2 = 45.75 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 = 45.75 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 45.75 + 2.640625 Combine like terms: 45.75 + 2.640625 = 48.390625 2.640625 + 3.25x + x2 = 48.390625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 48.390625 Calculate the square root of the right side: 6.956337039 Break this problem into two subproblems by setting (x + 1.625) equal to 6.956337039 and -6.956337039.Subproblem 1
x + 1.625 = 6.956337039 Simplifying x + 1.625 = 6.956337039 Reorder the terms: 1.625 + x = 6.956337039 Solving 1.625 + x = 6.956337039 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 = 6.956337039 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 6.956337039 + -1.625 x = 6.956337039 + -1.625 Combine like terms: 6.956337039 + -1.625 = 5.331337039 x = 5.331337039 Simplifying x = 5.331337039Subproblem 2
x + 1.625 = -6.956337039 Simplifying x + 1.625 = -6.956337039 Reorder the terms: 1.625 + x = -6.956337039 Solving 1.625 + x = -6.956337039 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 = -6.956337039 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -6.956337039 + -1.625 x = -6.956337039 + -1.625 Combine like terms: -6.956337039 + -1.625 = -8.581337039 x = -8.581337039 Simplifying x = -8.581337039Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.331337039, -8.581337039}Solution
x = {5.331337039, -8.581337039}
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