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Simplifying 8x2 + -43x + -18 = 0 Reorder the terms: -18 + -43x + 8x2 = 0 Solving -18 + -43x + 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'. -2.25 + -5.375x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -5.375x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -5.375x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -5.375x + x2 = 0 + 2.25 -5.375x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -5.375x + x2 = 2.25 The x term is -5.375x. Take half its coefficient (-2.6875). Square it (7.22265625) and add it to both sides. Add '7.22265625' to each side of the equation. -5.375x + 7.22265625 + x2 = 2.25 + 7.22265625 Reorder the terms: 7.22265625 + -5.375x + x2 = 2.25 + 7.22265625 Combine like terms: 2.25 + 7.22265625 = 9.47265625 7.22265625 + -5.375x + x2 = 9.47265625 Factor a perfect square on the left side: (x + -2.6875)(x + -2.6875) = 9.47265625 Calculate the square root of the right side: 3.077768063 Break this problem into two subproblems by setting (x + -2.6875) equal to 3.077768063 and -3.077768063.Subproblem 1
x + -2.6875 = 3.077768063 Simplifying x + -2.6875 = 3.077768063 Reorder the terms: -2.6875 + x = 3.077768063 Solving -2.6875 + x = 3.077768063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6875' to each side of the equation. -2.6875 + 2.6875 + x = 3.077768063 + 2.6875 Combine like terms: -2.6875 + 2.6875 = 0.0000 0.0000 + x = 3.077768063 + 2.6875 x = 3.077768063 + 2.6875 Combine like terms: 3.077768063 + 2.6875 = 5.765268063 x = 5.765268063 Simplifying x = 5.765268063Subproblem 2
x + -2.6875 = -3.077768063 Simplifying x + -2.6875 = -3.077768063 Reorder the terms: -2.6875 + x = -3.077768063 Solving -2.6875 + x = -3.077768063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6875' to each side of the equation. -2.6875 + 2.6875 + x = -3.077768063 + 2.6875 Combine like terms: -2.6875 + 2.6875 = 0.0000 0.0000 + x = -3.077768063 + 2.6875 x = -3.077768063 + 2.6875 Combine like terms: -3.077768063 + 2.6875 = -0.390268063 x = -0.390268063 Simplifying x = -0.390268063Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.765268063, -0.390268063}
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