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Simplifying 27x = 9x2 + 2 Reorder the terms: 27x = 2 + 9x2 Solving 27x = 2 + 9x2 Solving for variable 'x'. Reorder the terms: -2 + 27x + -9x2 = 2 + 9x2 + -2 + -9x2 Reorder the terms: -2 + 27x + -9x2 = 2 + -2 + 9x2 + -9x2 Combine like terms: 2 + -2 = 0 -2 + 27x + -9x2 = 0 + 9x2 + -9x2 -2 + 27x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -2 + 27x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.2222222222 + -3x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -3x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -3x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + -0.2222222222 -3x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -3x + x2 = -0.2222222222 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.2222222222 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.2222222222 + 2.25 Combine like terms: -0.2222222222 + 2.25 = 2.0277777778 2.25 + -3x + x2 = 2.0277777778 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.0277777778 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (x + -1.5) equal to 1.424000624 and -1.424000624.Subproblem 1
x + -1.5 = 1.424000624 Simplifying x + -1.5 = 1.424000624 Reorder the terms: -1.5 + x = 1.424000624 Solving -1.5 + x = 1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.424000624 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.424000624 + 1.5 x = 1.424000624 + 1.5 Combine like terms: 1.424000624 + 1.5 = 2.924000624 x = 2.924000624 Simplifying x = 2.924000624Subproblem 2
x + -1.5 = -1.424000624 Simplifying x + -1.5 = -1.424000624 Reorder the terms: -1.5 + x = -1.424000624 Solving -1.5 + x = -1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.424000624 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.424000624 + 1.5 x = -1.424000624 + 1.5 Combine like terms: -1.424000624 + 1.5 = 0.075999376 x = 0.075999376 Simplifying x = 0.075999376Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.924000624, 0.075999376}
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