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Simplifying 8x2 + 11x + -42 = 0 Reorder the terms: -42 + 11x + 8x2 = 0 Solving -42 + 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'. -5.25 + 1.375x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 1.375x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 1.375x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 1.375x + x2 = 0 + 5.25 1.375x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 1.375x + x2 = 5.25 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 = 5.25 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = 5.25 + 0.47265625 Combine like terms: 5.25 + 0.47265625 = 5.72265625 0.47265625 + 1.375x + x2 = 5.72265625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 5.72265625 Calculate the square root of the right side: 2.392207401 Break this problem into two subproblems by setting (x + 0.6875) equal to 2.392207401 and -2.392207401.Subproblem 1
x + 0.6875 = 2.392207401 Simplifying x + 0.6875 = 2.392207401 Reorder the terms: 0.6875 + x = 2.392207401 Solving 0.6875 + x = 2.392207401 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 = 2.392207401 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 2.392207401 + -0.6875 x = 2.392207401 + -0.6875 Combine like terms: 2.392207401 + -0.6875 = 1.704707401 x = 1.704707401 Simplifying x = 1.704707401Subproblem 2
x + 0.6875 = -2.392207401 Simplifying x + 0.6875 = -2.392207401 Reorder the terms: 0.6875 + x = -2.392207401 Solving 0.6875 + x = -2.392207401 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 = -2.392207401 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -2.392207401 + -0.6875 x = -2.392207401 + -0.6875 Combine like terms: -2.392207401 + -0.6875 = -3.079707401 x = -3.079707401 Simplifying x = -3.079707401Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.704707401, -3.079707401}
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