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Simplifying 9x2 + 54x = 1 Reorder the terms: 54x + 9x2 = 1 Solving 54x + 9x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 54x + 9x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 54x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.1111111111 + 6x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 6x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 6x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 6x + x2 = 0 + 0.1111111111 6x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 6x + x2 = 0.1111111111 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 = 0.1111111111 + 9 Reorder the terms: 9 + 6x + x2 = 0.1111111111 + 9 Combine like terms: 0.1111111111 + 9 = 9.1111111111 9 + 6x + x2 = 9.1111111111 Factor a perfect square on the left side: (x + 3)(x + 3) = 9.1111111111 Calculate the square root of the right side: 3.018461713 Break this problem into two subproblems by setting (x + 3) equal to 3.018461713 and -3.018461713.Subproblem 1
x + 3 = 3.018461713 Simplifying x + 3 = 3.018461713 Reorder the terms: 3 + x = 3.018461713 Solving 3 + x = 3.018461713 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 = 3.018461713 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.018461713 + -3 x = 3.018461713 + -3 Combine like terms: 3.018461713 + -3 = 0.018461713 x = 0.018461713 Simplifying x = 0.018461713Subproblem 2
x + 3 = -3.018461713 Simplifying x + 3 = -3.018461713 Reorder the terms: 3 + x = -3.018461713 Solving 3 + x = -3.018461713 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 = -3.018461713 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.018461713 + -3 x = -3.018461713 + -3 Combine like terms: -3.018461713 + -3 = -6.018461713 x = -6.018461713 Simplifying x = -6.018461713Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.018461713, -6.018461713}
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