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Simplifying 8x2 + -27x + -24 = 0 Reorder the terms: -24 + -27x + 8x2 = 0 Solving -24 + -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'. -3 + -3.375x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3.375x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -3.375x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3.375x + x2 = 0 + 3 -3.375x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3.375x + x2 = 3 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 = 3 + 2.84765625 Reorder the terms: 2.84765625 + -3.375x + x2 = 3 + 2.84765625 Combine like terms: 3 + 2.84765625 = 5.84765625 2.84765625 + -3.375x + x2 = 5.84765625 Factor a perfect square on the left side: (x + -1.6875)(x + -1.6875) = 5.84765625 Calculate the square root of the right side: 2.418192765 Break this problem into two subproblems by setting (x + -1.6875) equal to 2.418192765 and -2.418192765.Subproblem 1
x + -1.6875 = 2.418192765 Simplifying x + -1.6875 = 2.418192765 Reorder the terms: -1.6875 + x = 2.418192765 Solving -1.6875 + x = 2.418192765 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 = 2.418192765 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = 2.418192765 + 1.6875 x = 2.418192765 + 1.6875 Combine like terms: 2.418192765 + 1.6875 = 4.105692765 x = 4.105692765 Simplifying x = 4.105692765Subproblem 2
x + -1.6875 = -2.418192765 Simplifying x + -1.6875 = -2.418192765 Reorder the terms: -1.6875 + x = -2.418192765 Solving -1.6875 + x = -2.418192765 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 = -2.418192765 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = -2.418192765 + 1.6875 x = -2.418192765 + 1.6875 Combine like terms: -2.418192765 + 1.6875 = -0.730692765 x = -0.730692765 Simplifying x = -0.730692765Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.105692765, -0.730692765}
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