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Simplifying 9x2 + 54x + -47 = 0 Reorder the terms: -47 + 54x + 9x2 = 0 Solving -47 + 54x + 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'. -5.222222222 + 6x + x2 = 0 Move the constant term to the right: Add '5.222222222' to each side of the equation. -5.222222222 + 6x + 5.222222222 + x2 = 0 + 5.222222222 Reorder the terms: -5.222222222 + 5.222222222 + 6x + x2 = 0 + 5.222222222 Combine like terms: -5.222222222 + 5.222222222 = 0.000000000 0.000000000 + 6x + x2 = 0 + 5.222222222 6x + x2 = 0 + 5.222222222 Combine like terms: 0 + 5.222222222 = 5.222222222 6x + x2 = 5.222222222 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 5.222222222 + 9 Reorder the terms: 9 + 6x + x2 = 5.222222222 + 9 Combine like terms: 5.222222222 + 9 = 14.222222222 9 + 6x + x2 = 14.222222222 Factor a perfect square on the left side: (x + 3)(x + 3) = 14.222222222 Calculate the square root of the right side: 3.771236166 Break this problem into two subproblems by setting (x + 3) equal to 3.771236166 and -3.771236166.Subproblem 1
x + 3 = 3.771236166 Simplifying x + 3 = 3.771236166 Reorder the terms: 3 + x = 3.771236166 Solving 3 + x = 3.771236166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.771236166 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.771236166 + -3 x = 3.771236166 + -3 Combine like terms: 3.771236166 + -3 = 0.771236166 x = 0.771236166 Simplifying x = 0.771236166Subproblem 2
x + 3 = -3.771236166 Simplifying x + 3 = -3.771236166 Reorder the terms: 3 + x = -3.771236166 Solving 3 + x = -3.771236166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.771236166 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.771236166 + -3 x = -3.771236166 + -3 Combine like terms: -3.771236166 + -3 = -6.771236166 x = -6.771236166 Simplifying x = -6.771236166Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.771236166, -6.771236166}
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