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Simplifying 9x2 + 47x + -18 = 0 Reorder the terms: -18 + 47x + 9x2 = 0 Solving -18 + 47x + 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'. -2 + 5.222222222x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 5.222222222x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 5.222222222x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5.222222222x + x2 = 0 + 2 5.222222222x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 5.222222222x + x2 = 2 The x term is 5.222222222x. Take half its coefficient (2.611111111). Square it (6.817901234) and add it to both sides. Add '6.817901234' to each side of the equation. 5.222222222x + 6.817901234 + x2 = 2 + 6.817901234 Reorder the terms: 6.817901234 + 5.222222222x + x2 = 2 + 6.817901234 Combine like terms: 2 + 6.817901234 = 8.817901234 6.817901234 + 5.222222222x + x2 = 8.817901234 Factor a perfect square on the left side: (x + 2.611111111)(x + 2.611111111) = 8.817901234 Calculate the square root of the right side: 2.969495114 Break this problem into two subproblems by setting (x + 2.611111111) equal to 2.969495114 and -2.969495114.Subproblem 1
x + 2.611111111 = 2.969495114 Simplifying x + 2.611111111 = 2.969495114 Reorder the terms: 2.611111111 + x = 2.969495114 Solving 2.611111111 + x = 2.969495114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.611111111' to each side of the equation. 2.611111111 + -2.611111111 + x = 2.969495114 + -2.611111111 Combine like terms: 2.611111111 + -2.611111111 = 0.000000000 0.000000000 + x = 2.969495114 + -2.611111111 x = 2.969495114 + -2.611111111 Combine like terms: 2.969495114 + -2.611111111 = 0.358384003 x = 0.358384003 Simplifying x = 0.358384003Subproblem 2
x + 2.611111111 = -2.969495114 Simplifying x + 2.611111111 = -2.969495114 Reorder the terms: 2.611111111 + x = -2.969495114 Solving 2.611111111 + x = -2.969495114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.611111111' to each side of the equation. 2.611111111 + -2.611111111 + x = -2.969495114 + -2.611111111 Combine like terms: 2.611111111 + -2.611111111 = 0.000000000 0.000000000 + x = -2.969495114 + -2.611111111 x = -2.969495114 + -2.611111111 Combine like terms: -2.969495114 + -2.611111111 = -5.580606225 x = -5.580606225 Simplifying x = -5.580606225Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.358384003, -5.580606225}
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