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Simplifying 8x2 + 11x + -13 = 0 Reorder the terms: -13 + 11x + 8x2 = 0 Solving -13 + 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'. -1.625 + 1.375x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 1.375x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 1.375x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 1.375x + x2 = 0 + 1.625 1.375x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 1.375x + x2 = 1.625 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 = 1.625 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = 1.625 + 0.47265625 Combine like terms: 1.625 + 0.47265625 = 2.09765625 0.47265625 + 1.375x + x2 = 2.09765625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 2.09765625 Calculate the square root of the right side: 1.448328778 Break this problem into two subproblems by setting (x + 0.6875) equal to 1.448328778 and -1.448328778.Subproblem 1
x + 0.6875 = 1.448328778 Simplifying x + 0.6875 = 1.448328778 Reorder the terms: 0.6875 + x = 1.448328778 Solving 0.6875 + x = 1.448328778 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 = 1.448328778 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 1.448328778 + -0.6875 x = 1.448328778 + -0.6875 Combine like terms: 1.448328778 + -0.6875 = 0.760828778 x = 0.760828778 Simplifying x = 0.760828778Subproblem 2
x + 0.6875 = -1.448328778 Simplifying x + 0.6875 = -1.448328778 Reorder the terms: 0.6875 + x = -1.448328778 Solving 0.6875 + x = -1.448328778 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 = -1.448328778 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -1.448328778 + -0.6875 x = -1.448328778 + -0.6875 Combine like terms: -1.448328778 + -0.6875 = -2.135828778 x = -2.135828778 Simplifying x = -2.135828778Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.760828778, -2.135828778}
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