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Simplifying 8x2 + -59x + 40 = 0 Reorder the terms: 40 + -59x + 8x2 = 0 Solving 40 + -59x + 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'. 5 + -7.375x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -7.375x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -7.375x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7.375x + x2 = 0 + -5 -7.375x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -7.375x + x2 = -5 The x term is -7.375x. Take half its coefficient (-3.6875). Square it (13.59765625) and add it to both sides. Add '13.59765625' to each side of the equation. -7.375x + 13.59765625 + x2 = -5 + 13.59765625 Reorder the terms: 13.59765625 + -7.375x + x2 = -5 + 13.59765625 Combine like terms: -5 + 13.59765625 = 8.59765625 13.59765625 + -7.375x + x2 = 8.59765625 Factor a perfect square on the left side: (x + -3.6875)(x + -3.6875) = 8.59765625 Calculate the square root of the right side: 2.932176026 Break this problem into two subproblems by setting (x + -3.6875) equal to 2.932176026 and -2.932176026.Subproblem 1
x + -3.6875 = 2.932176026 Simplifying x + -3.6875 = 2.932176026 Reorder the terms: -3.6875 + x = 2.932176026 Solving -3.6875 + x = 2.932176026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + x = 2.932176026 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + x = 2.932176026 + 3.6875 x = 2.932176026 + 3.6875 Combine like terms: 2.932176026 + 3.6875 = 6.619676026 x = 6.619676026 Simplifying x = 6.619676026Subproblem 2
x + -3.6875 = -2.932176026 Simplifying x + -3.6875 = -2.932176026 Reorder the terms: -3.6875 + x = -2.932176026 Solving -3.6875 + x = -2.932176026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + x = -2.932176026 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + x = -2.932176026 + 3.6875 x = -2.932176026 + 3.6875 Combine like terms: -2.932176026 + 3.6875 = 0.755323974 x = 0.755323974 Simplifying x = 0.755323974Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.619676026, 0.755323974}
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