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Simplifying 8x2 + 54x + 9 = 0 Reorder the terms: 9 + 54x + 8x2 = 0 Solving 9 + 54x + 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 + 6.75x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + 6.75x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + 6.75x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + 6.75x + x2 = 0 + -1.125 6.75x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 6.75x + x2 = -1.125 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = -1.125 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = -1.125 + 11.390625 Combine like terms: -1.125 + 11.390625 = 10.265625 11.390625 + 6.75x + x2 = 10.265625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 10.265625 Calculate the square root of the right side: 3.204001404 Break this problem into two subproblems by setting (x + 3.375) equal to 3.204001404 and -3.204001404.Subproblem 1
x + 3.375 = 3.204001404 Simplifying x + 3.375 = 3.204001404 Reorder the terms: 3.375 + x = 3.204001404 Solving 3.375 + x = 3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = 3.204001404 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 3.204001404 + -3.375 x = 3.204001404 + -3.375 Combine like terms: 3.204001404 + -3.375 = -0.170998596 x = -0.170998596 Simplifying x = -0.170998596Subproblem 2
x + 3.375 = -3.204001404 Simplifying x + 3.375 = -3.204001404 Reorder the terms: 3.375 + x = -3.204001404 Solving 3.375 + x = -3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = -3.204001404 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -3.204001404 + -3.375 x = -3.204001404 + -3.375 Combine like terms: -3.204001404 + -3.375 = -6.579001404 x = -6.579001404 Simplifying x = -6.579001404Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.170998596, -6.579001404}
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