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Simplifying 8x2 + 55x + -9 = 0 Reorder the terms: -9 + 55x + 8x2 = 0 Solving -9 + 55x + 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'. -1.125 + 6.875x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 6.875x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 6.875x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 6.875x + x2 = 0 + 1.125 6.875x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 6.875x + x2 = 1.125 The x term is 6.875x. Take half its coefficient (3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. 6.875x + 11.81640625 + x2 = 1.125 + 11.81640625 Reorder the terms: 11.81640625 + 6.875x + x2 = 1.125 + 11.81640625 Combine like terms: 1.125 + 11.81640625 = 12.94140625 11.81640625 + 6.875x + x2 = 12.94140625 Factor a perfect square on the left side: (x + 3.4375)(x + 3.4375) = 12.94140625 Calculate the square root of the right side: 3.597416608 Break this problem into two subproblems by setting (x + 3.4375) equal to 3.597416608 and -3.597416608.Subproblem 1
x + 3.4375 = 3.597416608 Simplifying x + 3.4375 = 3.597416608 Reorder the terms: 3.4375 + x = 3.597416608 Solving 3.4375 + x = 3.597416608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4375' to each side of the equation. 3.4375 + -3.4375 + x = 3.597416608 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + x = 3.597416608 + -3.4375 x = 3.597416608 + -3.4375 Combine like terms: 3.597416608 + -3.4375 = 0.159916608 x = 0.159916608 Simplifying x = 0.159916608Subproblem 2
x + 3.4375 = -3.597416608 Simplifying x + 3.4375 = -3.597416608 Reorder the terms: 3.4375 + x = -3.597416608 Solving 3.4375 + x = -3.597416608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4375' to each side of the equation. 3.4375 + -3.4375 + x = -3.597416608 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + x = -3.597416608 + -3.4375 x = -3.597416608 + -3.4375 Combine like terms: -3.597416608 + -3.4375 = -7.034916608 x = -7.034916608 Simplifying x = -7.034916608Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.159916608, -7.034916608}
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