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Simplifying 8x2 + -41x + -65 = 0 Reorder the terms: -65 + -41x + 8x2 = 0 Solving -65 + -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'. -8.125 + -5.125x + x2 = 0 Move the constant term to the right: Add '8.125' to each side of the equation. -8.125 + -5.125x + 8.125 + x2 = 0 + 8.125 Reorder the terms: -8.125 + 8.125 + -5.125x + x2 = 0 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + -5.125x + x2 = 0 + 8.125 -5.125x + x2 = 0 + 8.125 Combine like terms: 0 + 8.125 = 8.125 -5.125x + x2 = 8.125 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 = 8.125 + 6.56640625 Reorder the terms: 6.56640625 + -5.125x + x2 = 8.125 + 6.56640625 Combine like terms: 8.125 + 6.56640625 = 14.69140625 6.56640625 + -5.125x + x2 = 14.69140625 Factor a perfect square on the left side: (x + -2.5625)(x + -2.5625) = 14.69140625 Calculate the square root of the right side: 3.832937027 Break this problem into two subproblems by setting (x + -2.5625) equal to 3.832937027 and -3.832937027.Subproblem 1
x + -2.5625 = 3.832937027 Simplifying x + -2.5625 = 3.832937027 Reorder the terms: -2.5625 + x = 3.832937027 Solving -2.5625 + x = 3.832937027 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 = 3.832937027 + 2.5625 Combine like terms: -2.5625 + 2.5625 = 0.0000 0.0000 + x = 3.832937027 + 2.5625 x = 3.832937027 + 2.5625 Combine like terms: 3.832937027 + 2.5625 = 6.395437027 x = 6.395437027 Simplifying x = 6.395437027Subproblem 2
x + -2.5625 = -3.832937027 Simplifying x + -2.5625 = -3.832937027 Reorder the terms: -2.5625 + x = -3.832937027 Solving -2.5625 + x = -3.832937027 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 = -3.832937027 + 2.5625 Combine like terms: -2.5625 + 2.5625 = 0.0000 0.0000 + x = -3.832937027 + 2.5625 x = -3.832937027 + 2.5625 Combine like terms: -3.832937027 + 2.5625 = -1.270437027 x = -1.270437027 Simplifying x = -1.270437027Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.395437027, -1.270437027}
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