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Simplifying 9x2 + 56x + 74 = 0 Reorder the terms: 74 + 56x + 9x2 = 0 Solving 74 + 56x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 8.222222222 + 6.222222222x + x2 = 0 Move the constant term to the right: Add '-8.222222222' to each side of the equation. 8.222222222 + 6.222222222x + -8.222222222 + x2 = 0 + -8.222222222 Reorder the terms: 8.222222222 + -8.222222222 + 6.222222222x + x2 = 0 + -8.222222222 Combine like terms: 8.222222222 + -8.222222222 = 0.000000000 0.000000000 + 6.222222222x + x2 = 0 + -8.222222222 6.222222222x + x2 = 0 + -8.222222222 Combine like terms: 0 + -8.222222222 = -8.222222222 6.222222222x + x2 = -8.222222222 The x term is 6.222222222x. Take half its coefficient (3.111111111). Square it (9.679012345) and add it to both sides. Add '9.679012345' to each side of the equation. 6.222222222x + 9.679012345 + x2 = -8.222222222 + 9.679012345 Reorder the terms: 9.679012345 + 6.222222222x + x2 = -8.222222222 + 9.679012345 Combine like terms: -8.222222222 + 9.679012345 = 1.456790123 9.679012345 + 6.222222222x + x2 = 1.456790123 Factor a perfect square on the left side: (x + 3.111111111)(x + 3.111111111) = 1.456790123 Calculate the square root of the right side: 1.20697561 Break this problem into two subproblems by setting (x + 3.111111111) equal to 1.20697561 and -1.20697561.Subproblem 1
x + 3.111111111 = 1.20697561 Simplifying x + 3.111111111 = 1.20697561 Reorder the terms: 3.111111111 + x = 1.20697561 Solving 3.111111111 + x = 1.20697561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.111111111' to each side of the equation. 3.111111111 + -3.111111111 + x = 1.20697561 + -3.111111111 Combine like terms: 3.111111111 + -3.111111111 = 0.000000000 0.000000000 + x = 1.20697561 + -3.111111111 x = 1.20697561 + -3.111111111 Combine like terms: 1.20697561 + -3.111111111 = -1.904135501 x = -1.904135501 Simplifying x = -1.904135501Subproblem 2
x + 3.111111111 = -1.20697561 Simplifying x + 3.111111111 = -1.20697561 Reorder the terms: 3.111111111 + x = -1.20697561 Solving 3.111111111 + x = -1.20697561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.111111111' to each side of the equation. 3.111111111 + -3.111111111 + x = -1.20697561 + -3.111111111 Combine like terms: 3.111111111 + -3.111111111 = 0.000000000 0.000000000 + x = -1.20697561 + -3.111111111 x = -1.20697561 + -3.111111111 Combine like terms: -1.20697561 + -3.111111111 = -4.318086721 x = -4.318086721 Simplifying x = -4.318086721Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.904135501, -4.318086721}
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