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Simplifying 8x2 + -41x + 15 = 0 Reorder the terms: 15 + -41x + 8x2 = 0 Solving 15 + -41x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.875 + -5.125x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -5.125x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -5.125x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -5.125x + x2 = 0 + -1.875 -5.125x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -5.125x + x2 = -1.875 The x term is -5.125x. Take half its coefficient (-2.5625). Square it (6.56640625) and add it to both sides. Add '6.56640625' to each side of the equation. -5.125x + 6.56640625 + x2 = -1.875 + 6.56640625 Reorder the terms: 6.56640625 + -5.125x + x2 = -1.875 + 6.56640625 Combine like terms: -1.875 + 6.56640625 = 4.69140625 6.56640625 + -5.125x + x2 = 4.69140625 Factor a perfect square on the left side: (x + -2.5625)(x + -2.5625) = 4.69140625 Calculate the square root of the right side: 2.165965431 Break this problem into two subproblems by setting (x + -2.5625) equal to 2.165965431 and -2.165965431.Subproblem 1
x + -2.5625 = 2.165965431 Simplifying x + -2.5625 = 2.165965431 Reorder the terms: -2.5625 + x = 2.165965431 Solving -2.5625 + x = 2.165965431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5625' to each side of the equation. -2.5625 + 2.5625 + x = 2.165965431 + 2.5625 Combine like terms: -2.5625 + 2.5625 = 0.0000 0.0000 + x = 2.165965431 + 2.5625 x = 2.165965431 + 2.5625 Combine like terms: 2.165965431 + 2.5625 = 4.728465431 x = 4.728465431 Simplifying x = 4.728465431Subproblem 2
x + -2.5625 = -2.165965431 Simplifying x + -2.5625 = -2.165965431 Reorder the terms: -2.5625 + x = -2.165965431 Solving -2.5625 + x = -2.165965431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5625' to each side of the equation. -2.5625 + 2.5625 + x = -2.165965431 + 2.5625 Combine like terms: -2.5625 + 2.5625 = 0.0000 0.0000 + x = -2.165965431 + 2.5625 x = -2.165965431 + 2.5625 Combine like terms: -2.165965431 + 2.5625 = 0.396534569 x = 0.396534569 Simplifying x = 0.396534569Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.728465431, 0.396534569}
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