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Simplifying -8x2 + 59x + -8 = 0 Reorder the terms: -8 + 59x + -8x2 = 0 Solving -8 + 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'. 1 + -7.375x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -7.375x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -7.375x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7.375x + x2 = 0 + -1 -7.375x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -7.375x + x2 = -1 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 = -1 + 13.59765625 Reorder the terms: 13.59765625 + -7.375x + x2 = -1 + 13.59765625 Combine like terms: -1 + 13.59765625 = 12.59765625 13.59765625 + -7.375x + x2 = 12.59765625 Factor a perfect square on the left side: (x + -3.6875)(x + -3.6875) = 12.59765625 Calculate the square root of the right side: 3.549317716 Break this problem into two subproblems by setting (x + -3.6875) equal to 3.549317716 and -3.549317716.Subproblem 1
x + -3.6875 = 3.549317716 Simplifying x + -3.6875 = 3.549317716 Reorder the terms: -3.6875 + x = 3.549317716 Solving -3.6875 + x = 3.549317716 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 = 3.549317716 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + x = 3.549317716 + 3.6875 x = 3.549317716 + 3.6875 Combine like terms: 3.549317716 + 3.6875 = 7.236817716 x = 7.236817716 Simplifying x = 7.236817716Subproblem 2
x + -3.6875 = -3.549317716 Simplifying x + -3.6875 = -3.549317716 Reorder the terms: -3.6875 + x = -3.549317716 Solving -3.6875 + x = -3.549317716 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 = -3.549317716 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + x = -3.549317716 + 3.6875 x = -3.549317716 + 3.6875 Combine like terms: -3.549317716 + 3.6875 = 0.138182284 x = 0.138182284 Simplifying x = 0.138182284Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.236817716, 0.138182284}
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