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Simplifying 8x2 + 27x + -14 = 0 Reorder the terms: -14 + 27x + 8x2 = 0 Solving -14 + 27x + 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'. -1.75 + 3.375x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 3.375x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 3.375x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 3.375x + x2 = 0 + 1.75 3.375x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 3.375x + x2 = 1.75 The x term is 3.375x. Take half its coefficient (1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. 3.375x + 2.84765625 + x2 = 1.75 + 2.84765625 Reorder the terms: 2.84765625 + 3.375x + x2 = 1.75 + 2.84765625 Combine like terms: 1.75 + 2.84765625 = 4.59765625 2.84765625 + 3.375x + x2 = 4.59765625 Factor a perfect square on the left side: (x + 1.6875)(x + 1.6875) = 4.59765625 Calculate the square root of the right side: 2.1442146 Break this problem into two subproblems by setting (x + 1.6875) equal to 2.1442146 and -2.1442146.Subproblem 1
x + 1.6875 = 2.1442146 Simplifying x + 1.6875 = 2.1442146 Reorder the terms: 1.6875 + x = 2.1442146 Solving 1.6875 + x = 2.1442146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6875' to each side of the equation. 1.6875 + -1.6875 + x = 2.1442146 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = 2.1442146 + -1.6875 x = 2.1442146 + -1.6875 Combine like terms: 2.1442146 + -1.6875 = 0.4567146 x = 0.4567146 Simplifying x = 0.4567146Subproblem 2
x + 1.6875 = -2.1442146 Simplifying x + 1.6875 = -2.1442146 Reorder the terms: 1.6875 + x = -2.1442146 Solving 1.6875 + x = -2.1442146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6875' to each side of the equation. 1.6875 + -1.6875 + x = -2.1442146 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = -2.1442146 + -1.6875 x = -2.1442146 + -1.6875 Combine like terms: -2.1442146 + -1.6875 = -3.8317146 x = -3.8317146 Simplifying x = -3.8317146Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4567146, -3.8317146}
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