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Simplifying 8x2 + -27x + -24 = -6 Reorder the terms: -24 + -27x + 8x2 = -6 Solving -24 + -27x + 8x2 = -6 Solving for variable 'x'. Reorder the terms: -24 + 6 + -27x + 8x2 = -6 + 6 Combine like terms: -24 + 6 = -18 -18 + -27x + 8x2 = -6 + 6 Combine like terms: -6 + 6 = 0 -18 + -27x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.25 + -3.375x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -3.375x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -3.375x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -3.375x + x2 = 0 + 2.25 -3.375x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -3.375x + x2 = 2.25 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 = 2.25 + 2.84765625 Reorder the terms: 2.84765625 + -3.375x + x2 = 2.25 + 2.84765625 Combine like terms: 2.25 + 2.84765625 = 5.09765625 2.84765625 + -3.375x + x2 = 5.09765625 Factor a perfect square on the left side: (x + -1.6875)(x + -1.6875) = 5.09765625 Calculate the square root of the right side: 2.257798984 Break this problem into two subproblems by setting (x + -1.6875) equal to 2.257798984 and -2.257798984.Subproblem 1
x + -1.6875 = 2.257798984 Simplifying x + -1.6875 = 2.257798984 Reorder the terms: -1.6875 + x = 2.257798984 Solving -1.6875 + x = 2.257798984 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 = 2.257798984 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = 2.257798984 + 1.6875 x = 2.257798984 + 1.6875 Combine like terms: 2.257798984 + 1.6875 = 3.945298984 x = 3.945298984 Simplifying x = 3.945298984Subproblem 2
x + -1.6875 = -2.257798984 Simplifying x + -1.6875 = -2.257798984 Reorder the terms: -1.6875 + x = -2.257798984 Solving -1.6875 + x = -2.257798984 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 = -2.257798984 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = -2.257798984 + 1.6875 x = -2.257798984 + 1.6875 Combine like terms: -2.257798984 + 1.6875 = -0.570298984 x = -0.570298984 Simplifying x = -0.570298984Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.945298984, -0.570298984}
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