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Simplifying 8x2 + 6x + 20x + 1 = 5 Reorder the terms: 1 + 6x + 20x + 8x2 = 5 Combine like terms: 6x + 20x = 26x 1 + 26x + 8x2 = 5 Solving 1 + 26x + 8x2 = 5 Solving for variable 'x'. Reorder the terms: 1 + -5 + 26x + 8x2 = 5 + -5 Combine like terms: 1 + -5 = -4 -4 + 26x + 8x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -4 + 26x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 13x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 13x + 4x2)' equal to zero and attempt to solve: Simplifying -2 + 13x + 4x2 = 0 Solving -2 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + 3.25x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 3.25x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 3.25x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 3.25x + x2 = 0 + 0.5 3.25x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 3.25x + x2 = 0.5 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 = 0.5 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 0.5 + 2.640625 Combine like terms: 0.5 + 2.640625 = 3.140625 2.640625 + 3.25x + x2 = 3.140625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + 1.625) equal to 1.77218086 and -1.77218086.Subproblem 1
x + 1.625 = 1.77218086 Simplifying x + 1.625 = 1.77218086 Reorder the terms: 1.625 + x = 1.77218086 Solving 1.625 + x = 1.77218086 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 = 1.77218086 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 1.77218086 + -1.625 x = 1.77218086 + -1.625 Combine like terms: 1.77218086 + -1.625 = 0.14718086 x = 0.14718086 Simplifying x = 0.14718086Subproblem 2
x + 1.625 = -1.77218086 Simplifying x + 1.625 = -1.77218086 Reorder the terms: 1.625 + x = -1.77218086 Solving 1.625 + x = -1.77218086 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 = -1.77218086 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -1.77218086 + -1.625 x = -1.77218086 + -1.625 Combine like terms: -1.77218086 + -1.625 = -3.39718086 x = -3.39718086 Simplifying x = -3.39718086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.14718086, -3.39718086}Solution
x = {0.14718086, -3.39718086}
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