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Simplifying 4x2 + -61x + -24 = 0 Reorder the terms: -24 + -61x + 4x2 = 0 Solving -24 + -61x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6 + -15.25x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -15.25x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -15.25x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -15.25x + x2 = 0 + 6 -15.25x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -15.25x + x2 = 6 The x term is -15.25x. Take half its coefficient (-7.625). Square it (58.140625) and add it to both sides. Add '58.140625' to each side of the equation. -15.25x + 58.140625 + x2 = 6 + 58.140625 Reorder the terms: 58.140625 + -15.25x + x2 = 6 + 58.140625 Combine like terms: 6 + 58.140625 = 64.140625 58.140625 + -15.25x + x2 = 64.140625 Factor a perfect square on the left side: (x + -7.625)(x + -7.625) = 64.140625 Calculate the square root of the right side: 8.00878424 Break this problem into two subproblems by setting (x + -7.625) equal to 8.00878424 and -8.00878424.Subproblem 1
x + -7.625 = 8.00878424 Simplifying x + -7.625 = 8.00878424 Reorder the terms: -7.625 + x = 8.00878424 Solving -7.625 + x = 8.00878424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.625' to each side of the equation. -7.625 + 7.625 + x = 8.00878424 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + x = 8.00878424 + 7.625 x = 8.00878424 + 7.625 Combine like terms: 8.00878424 + 7.625 = 15.63378424 x = 15.63378424 Simplifying x = 15.63378424Subproblem 2
x + -7.625 = -8.00878424 Simplifying x + -7.625 = -8.00878424 Reorder the terms: -7.625 + x = -8.00878424 Solving -7.625 + x = -8.00878424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.625' to each side of the equation. -7.625 + 7.625 + x = -8.00878424 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + x = -8.00878424 + 7.625 x = -8.00878424 + 7.625 Combine like terms: -8.00878424 + 7.625 = -0.38378424 x = -0.38378424 Simplifying x = -0.38378424Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.63378424, -0.38378424}
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