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Simplifying 8x2 + -59x + -21 = 0 Reorder the terms: -21 + -59x + 8x2 = 0 Solving -21 + -59x + 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'. -2.625 + -7.375x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + -7.375x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + -7.375x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + -7.375x + x2 = 0 + 2.625 -7.375x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 -7.375x + x2 = 2.625 The x term is -7.375x. Take half its coefficient (-3.6875). Square it (13.59765625) and add it to both sides. Add '13.59765625' to each side of the equation. -7.375x + 13.59765625 + x2 = 2.625 + 13.59765625 Reorder the terms: 13.59765625 + -7.375x + x2 = 2.625 + 13.59765625 Combine like terms: 2.625 + 13.59765625 = 16.22265625 13.59765625 + -7.375x + x2 = 16.22265625 Factor a perfect square on the left side: (x + -3.6875)(x + -3.6875) = 16.22265625 Calculate the square root of the right side: 4.027735871 Break this problem into two subproblems by setting (x + -3.6875) equal to 4.027735871 and -4.027735871.Subproblem 1
x + -3.6875 = 4.027735871 Simplifying x + -3.6875 = 4.027735871 Reorder the terms: -3.6875 + x = 4.027735871 Solving -3.6875 + x = 4.027735871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + x = 4.027735871 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + x = 4.027735871 + 3.6875 x = 4.027735871 + 3.6875 Combine like terms: 4.027735871 + 3.6875 = 7.715235871 x = 7.715235871 Simplifying x = 7.715235871Subproblem 2
x + -3.6875 = -4.027735871 Simplifying x + -3.6875 = -4.027735871 Reorder the terms: -3.6875 + x = -4.027735871 Solving -3.6875 + x = -4.027735871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + x = -4.027735871 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + x = -4.027735871 + 3.6875 x = -4.027735871 + 3.6875 Combine like terms: -4.027735871 + 3.6875 = -0.340235871 x = -0.340235871 Simplifying x = -0.340235871Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.715235871, -0.340235871}
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