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Simplifying 3x2 + 54x + 233 = 0 Reorder the terms: 233 + 54x + 3x2 = 0 Solving 233 + 54x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 77.66666667 + 18x + x2 = 0 Move the constant term to the right: Add '-77.66666667' to each side of the equation. 77.66666667 + 18x + -77.66666667 + x2 = 0 + -77.66666667 Reorder the terms: 77.66666667 + -77.66666667 + 18x + x2 = 0 + -77.66666667 Combine like terms: 77.66666667 + -77.66666667 = 0.00000000 0.00000000 + 18x + x2 = 0 + -77.66666667 18x + x2 = 0 + -77.66666667 Combine like terms: 0 + -77.66666667 = -77.66666667 18x + x2 = -77.66666667 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -77.66666667 + 81 Reorder the terms: 81 + 18x + x2 = -77.66666667 + 81 Combine like terms: -77.66666667 + 81 = 3.33333333 81 + 18x + x2 = 3.33333333 Factor a perfect square on the left side: (x + 9)(x + 9) = 3.33333333 Calculate the square root of the right side: 1.825741857 Break this problem into two subproblems by setting (x + 9) equal to 1.825741857 and -1.825741857.Subproblem 1
x + 9 = 1.825741857 Simplifying x + 9 = 1.825741857 Reorder the terms: 9 + x = 1.825741857 Solving 9 + x = 1.825741857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 1.825741857 + -9 Combine like terms: 9 + -9 = 0 0 + x = 1.825741857 + -9 x = 1.825741857 + -9 Combine like terms: 1.825741857 + -9 = -7.174258143 x = -7.174258143 Simplifying x = -7.174258143Subproblem 2
x + 9 = -1.825741857 Simplifying x + 9 = -1.825741857 Reorder the terms: 9 + x = -1.825741857 Solving 9 + x = -1.825741857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -1.825741857 + -9 Combine like terms: 9 + -9 = 0 0 + x = -1.825741857 + -9 x = -1.825741857 + -9 Combine like terms: -1.825741857 + -9 = -10.825741857 x = -10.825741857 Simplifying x = -10.825741857Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.174258143, -10.825741857}
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