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Simplifying 8x2 + -11x + -24 = 0 Reorder the terms: -24 + -11x + 8x2 = 0 Solving -24 + -11x + 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 + -1.375x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.375x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1.375x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.375x + x2 = 0 + 3 -1.375x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.375x + x2 = 3 The x term is -1.375x. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375x + 0.47265625 + x2 = 3 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = 3 + 0.47265625 Combine like terms: 3 + 0.47265625 = 3.47265625 0.47265625 + -1.375x + x2 = 3.47265625 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = 3.47265625 Calculate the square root of the right side: 1.863506439 Break this problem into two subproblems by setting (x + -0.6875) equal to 1.863506439 and -1.863506439.Subproblem 1
x + -0.6875 = 1.863506439 Simplifying x + -0.6875 = 1.863506439 Reorder the terms: -0.6875 + x = 1.863506439 Solving -0.6875 + x = 1.863506439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = 1.863506439 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 1.863506439 + 0.6875 x = 1.863506439 + 0.6875 Combine like terms: 1.863506439 + 0.6875 = 2.551006439 x = 2.551006439 Simplifying x = 2.551006439Subproblem 2
x + -0.6875 = -1.863506439 Simplifying x + -0.6875 = -1.863506439 Reorder the terms: -0.6875 + x = -1.863506439 Solving -0.6875 + x = -1.863506439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = -1.863506439 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -1.863506439 + 0.6875 x = -1.863506439 + 0.6875 Combine like terms: -1.863506439 + 0.6875 = -1.176006439 x = -1.176006439 Simplifying x = -1.176006439Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.551006439, -1.176006439}
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