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Simplifying 8x2 + -11x + -52 = 0 Reorder the terms: -52 + -11x + 8x2 = 0 Solving -52 + -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'. -6.5 + -1.375x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -1.375x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -1.375x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -1.375x + x2 = 0 + 6.5 -1.375x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -1.375x + x2 = 6.5 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 = 6.5 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = 6.5 + 0.47265625 Combine like terms: 6.5 + 0.47265625 = 6.97265625 0.47265625 + -1.375x + x2 = 6.97265625 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = 6.97265625 Calculate the square root of the right side: 2.640578772 Break this problem into two subproblems by setting (x + -0.6875) equal to 2.640578772 and -2.640578772.Subproblem 1
x + -0.6875 = 2.640578772 Simplifying x + -0.6875 = 2.640578772 Reorder the terms: -0.6875 + x = 2.640578772 Solving -0.6875 + x = 2.640578772 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 = 2.640578772 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 2.640578772 + 0.6875 x = 2.640578772 + 0.6875 Combine like terms: 2.640578772 + 0.6875 = 3.328078772 x = 3.328078772 Simplifying x = 3.328078772Subproblem 2
x + -0.6875 = -2.640578772 Simplifying x + -0.6875 = -2.640578772 Reorder the terms: -0.6875 + x = -2.640578772 Solving -0.6875 + x = -2.640578772 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 = -2.640578772 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -2.640578772 + 0.6875 x = -2.640578772 + 0.6875 Combine like terms: -2.640578772 + 0.6875 = -1.953078772 x = -1.953078772 Simplifying x = -1.953078772Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.328078772, -1.953078772}
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