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Simplifying 9x2 + 29x + -12 = 0 Reorder the terms: -12 + 29x + 9x2 = 0 Solving -12 + 29x + 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'. -1.333333333 + 3.222222222x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 3.222222222x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 3.222222222x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 3.222222222x + x2 = 0 + 1.333333333 3.222222222x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 3.222222222x + x2 = 1.333333333 The x term is 3.222222222x. Take half its coefficient (1.611111111). Square it (2.595679012) and add it to both sides. Add '2.595679012' to each side of the equation. 3.222222222x + 2.595679012 + x2 = 1.333333333 + 2.595679012 Reorder the terms: 2.595679012 + 3.222222222x + x2 = 1.333333333 + 2.595679012 Combine like terms: 1.333333333 + 2.595679012 = 3.929012345 2.595679012 + 3.222222222x + x2 = 3.929012345 Factor a perfect square on the left side: (x + 1.611111111)(x + 1.611111111) = 3.929012345 Calculate the square root of the right side: 1.982173641 Break this problem into two subproblems by setting (x + 1.611111111) equal to 1.982173641 and -1.982173641.Subproblem 1
x + 1.611111111 = 1.982173641 Simplifying x + 1.611111111 = 1.982173641 Reorder the terms: 1.611111111 + x = 1.982173641 Solving 1.611111111 + x = 1.982173641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + x = 1.982173641 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + x = 1.982173641 + -1.611111111 x = 1.982173641 + -1.611111111 Combine like terms: 1.982173641 + -1.611111111 = 0.37106253 x = 0.37106253 Simplifying x = 0.37106253Subproblem 2
x + 1.611111111 = -1.982173641 Simplifying x + 1.611111111 = -1.982173641 Reorder the terms: 1.611111111 + x = -1.982173641 Solving 1.611111111 + x = -1.982173641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + x = -1.982173641 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + x = -1.982173641 + -1.611111111 x = -1.982173641 + -1.611111111 Combine like terms: -1.982173641 + -1.611111111 = -3.593284752 x = -3.593284752 Simplifying x = -3.593284752Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.37106253, -3.593284752}
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