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Simplifying 8x2 + 42x + -27 = 0 Reorder the terms: -27 + 42x + 8x2 = 0 Solving -27 + 42x + 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'. -3.375 + 5.25x + x2 = 0 Move the constant term to the right: Add '3.375' to each side of the equation. -3.375 + 5.25x + 3.375 + x2 = 0 + 3.375 Reorder the terms: -3.375 + 3.375 + 5.25x + x2 = 0 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + 5.25x + x2 = 0 + 3.375 5.25x + x2 = 0 + 3.375 Combine like terms: 0 + 3.375 = 3.375 5.25x + x2 = 3.375 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = 3.375 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = 3.375 + 6.890625 Combine like terms: 3.375 + 6.890625 = 10.265625 6.890625 + 5.25x + x2 = 10.265625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 10.265625 Calculate the square root of the right side: 3.204001404 Break this problem into two subproblems by setting (x + 2.625) equal to 3.204001404 and -3.204001404.Subproblem 1
x + 2.625 = 3.204001404 Simplifying x + 2.625 = 3.204001404 Reorder the terms: 2.625 + x = 3.204001404 Solving 2.625 + x = 3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 3.204001404 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 3.204001404 + -2.625 x = 3.204001404 + -2.625 Combine like terms: 3.204001404 + -2.625 = 0.579001404 x = 0.579001404 Simplifying x = 0.579001404Subproblem 2
x + 2.625 = -3.204001404 Simplifying x + 2.625 = -3.204001404 Reorder the terms: 2.625 + x = -3.204001404 Solving 2.625 + x = -3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -3.204001404 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -3.204001404 + -2.625 x = -3.204001404 + -2.625 Combine like terms: -3.204001404 + -2.625 = -5.829001404 x = -5.829001404 Simplifying x = -5.829001404Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.579001404, -5.829001404}
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