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Simplifying 9x2 + -2x + -54 = 0 Reorder the terms: -54 + -2x + 9x2 = 0 Solving -54 + -2x + 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'. -6 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.2222222222x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -0.2222222222x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.2222222222x + x2 = 0 + 6 -0.2222222222x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.2222222222x + x2 = 6 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = 6 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 6 + 0.01234567901 Combine like terms: 6 + 0.01234567901 = 6.01234567901 0.01234567901 + -0.2222222222x + x2 = 6.01234567901 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 6.01234567901 Calculate the square root of the right side: 2.452008499 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 2.452008499 and -2.452008499.Subproblem 1
x + -0.1111111111 = 2.452008499 Simplifying x + -0.1111111111 = 2.452008499 Reorder the terms: -0.1111111111 + x = 2.452008499 Solving -0.1111111111 + x = 2.452008499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 2.452008499 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 2.452008499 + 0.1111111111 x = 2.452008499 + 0.1111111111 Combine like terms: 2.452008499 + 0.1111111111 = 2.5631196101 x = 2.5631196101 Simplifying x = 2.5631196101Subproblem 2
x + -0.1111111111 = -2.452008499 Simplifying x + -0.1111111111 = -2.452008499 Reorder the terms: -0.1111111111 + x = -2.452008499 Solving -0.1111111111 + x = -2.452008499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -2.452008499 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -2.452008499 + 0.1111111111 x = -2.452008499 + 0.1111111111 Combine like terms: -2.452008499 + 0.1111111111 = -2.3408973879 x = -2.3408973879 Simplifying x = -2.3408973879Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5631196101, -2.3408973879}
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