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Simplifying 8x2 + 11x + -110 = 0 Reorder the terms: -110 + 11x + 8x2 = 0 Solving -110 + 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'. -13.75 + 1.375x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + 1.375x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + 1.375x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + 1.375x + x2 = 0 + 13.75 1.375x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 1.375x + x2 = 13.75 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 = 13.75 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = 13.75 + 0.47265625 Combine like terms: 13.75 + 0.47265625 = 14.22265625 0.47265625 + 1.375x + x2 = 14.22265625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 14.22265625 Calculate the square root of the right side: 3.77129371 Break this problem into two subproblems by setting (x + 0.6875) equal to 3.77129371 and -3.77129371.Subproblem 1
x + 0.6875 = 3.77129371 Simplifying x + 0.6875 = 3.77129371 Reorder the terms: 0.6875 + x = 3.77129371 Solving 0.6875 + x = 3.77129371 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 = 3.77129371 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 3.77129371 + -0.6875 x = 3.77129371 + -0.6875 Combine like terms: 3.77129371 + -0.6875 = 3.08379371 x = 3.08379371 Simplifying x = 3.08379371Subproblem 2
x + 0.6875 = -3.77129371 Simplifying x + 0.6875 = -3.77129371 Reorder the terms: 0.6875 + x = -3.77129371 Solving 0.6875 + x = -3.77129371 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 = -3.77129371 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -3.77129371 + -0.6875 x = -3.77129371 + -0.6875 Combine like terms: -3.77129371 + -0.6875 = -4.45879371 x = -4.45879371 Simplifying x = -4.45879371Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.08379371, -4.45879371}
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