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Simplifying (49x2) = 3x + 39 Reorder the terms: (49x2) = 39 + 3x Solving (49x2) = 39 + 3x Solving for variable 'x'. Reorder the terms: -39 + -3x + (49x2) = 39 + 3x + -39 + -3x Reorder the terms: -39 + -3x + (49x2) = 39 + -39 + 3x + -3x Combine like terms: 39 + -39 = 0 -39 + -3x + (49x2) = 0 + 3x + -3x -39 + -3x + (49x2) = 3x + -3x Combine like terms: 3x + -3x = 0 -39 + -3x + (49x2) = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.7959183673 + -0.0612244898x + x2 = 0 Move the constant term to the right: Add '0.7959183673' to each side of the equation. -0.7959183673 + -0.0612244898x + 0.7959183673 + x2 = 0 + 0.7959183673 Reorder the terms: -0.7959183673 + 0.7959183673 + -0.0612244898x + x2 = 0 + 0.7959183673 Combine like terms: -0.7959183673 + 0.7959183673 = 0.0000000000 0.0000000000 + -0.0612244898x + x2 = 0 + 0.7959183673 -0.0612244898x + x2 = 0 + 0.7959183673 Combine like terms: 0 + 0.7959183673 = 0.7959183673 -0.0612244898x + x2 = 0.7959183673 The x term is -0.0612244898x. Take half its coefficient (-0.0306122449). Square it (0.0009371095378) and add it to both sides. Add '0.0009371095378' to each side of the equation. -0.0612244898x + 0.0009371095378 + x2 = 0.7959183673 + 0.0009371095378 Reorder the terms: 0.0009371095378 + -0.0612244898x + x2 = 0.7959183673 + 0.0009371095378 Combine like terms: 0.7959183673 + 0.0009371095378 = 0.7968554768378 0.0009371095378 + -0.0612244898x + x2 = 0.7968554768378 Factor a perfect square on the left side: ((x) + -0.0306122449)((x) + -0.0306122449) = 0.7968554768378 Calculate the square root of the right side: 0.892667618 Break this problem into two subproblems by setting ((x) + -0.0306122449) equal to 0.892667618 and -0.892667618.Subproblem 1
(x) + -0.0306122449 = 0.892667618 Simplifying (x) + -0.0306122449 = 0.892667618 x + -0.0306122449 = 0.892667618 Reorder the terms: -0.0306122449 + x = 0.892667618 Solving -0.0306122449 + x = 0.892667618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0306122449' to each side of the equation. -0.0306122449 + 0.0306122449 + x = 0.892667618 + 0.0306122449 Combine like terms: -0.0306122449 + 0.0306122449 = 0.0000000000 0.0000000000 + x = 0.892667618 + 0.0306122449 x = 0.892667618 + 0.0306122449 Combine like terms: 0.892667618 + 0.0306122449 = 0.9232798629 x = 0.9232798629 Simplifying x = 0.9232798629Subproblem 2
(x) + -0.0306122449 = -0.892667618 Simplifying (x) + -0.0306122449 = -0.892667618 x + -0.0306122449 = -0.892667618 Reorder the terms: -0.0306122449 + x = -0.892667618 Solving -0.0306122449 + x = -0.892667618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0306122449' to each side of the equation. -0.0306122449 + 0.0306122449 + x = -0.892667618 + 0.0306122449 Combine like terms: -0.0306122449 + 0.0306122449 = 0.0000000000 0.0000000000 + x = -0.892667618 + 0.0306122449 x = -0.892667618 + 0.0306122449 Combine like terms: -0.892667618 + 0.0306122449 = -0.8620553731 x = -0.8620553731 Simplifying x = -0.8620553731Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9232798629, -0.8620553731}
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