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Simplifying 27x2 + -39x + 8 = 0 Reorder the terms: 8 + -39x + 27x2 = 0 Solving 8 + -39x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.2962962963 + -1.444444444x + x2 = 0 Move the constant term to the right: Add '-0.2962962963' to each side of the equation. 0.2962962963 + -1.444444444x + -0.2962962963 + x2 = 0 + -0.2962962963 Reorder the terms: 0.2962962963 + -0.2962962963 + -1.444444444x + x2 = 0 + -0.2962962963 Combine like terms: 0.2962962963 + -0.2962962963 = 0.0000000000 0.0000000000 + -1.444444444x + x2 = 0 + -0.2962962963 -1.444444444x + x2 = 0 + -0.2962962963 Combine like terms: 0 + -0.2962962963 = -0.2962962963 -1.444444444x + x2 = -0.2962962963 The x term is -1.444444444x. Take half its coefficient (-0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. -1.444444444x + 0.5216049380 + x2 = -0.2962962963 + 0.5216049380 Reorder the terms: 0.5216049380 + -1.444444444x + x2 = -0.2962962963 + 0.5216049380 Combine like terms: -0.2962962963 + 0.5216049380 = 0.2253086417 0.5216049380 + -1.444444444x + x2 = 0.2253086417 Factor a perfect square on the left side: (x + -0.722222222)(x + -0.722222222) = 0.2253086417 Calculate the square root of the right side: 0.474666874 Break this problem into two subproblems by setting (x + -0.722222222) equal to 0.474666874 and -0.474666874.Subproblem 1
x + -0.722222222 = 0.474666874 Simplifying x + -0.722222222 = 0.474666874 Reorder the terms: -0.722222222 + x = 0.474666874 Solving -0.722222222 + x = 0.474666874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = 0.474666874 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = 0.474666874 + 0.722222222 x = 0.474666874 + 0.722222222 Combine like terms: 0.474666874 + 0.722222222 = 1.196889096 x = 1.196889096 Simplifying x = 1.196889096Subproblem 2
x + -0.722222222 = -0.474666874 Simplifying x + -0.722222222 = -0.474666874 Reorder the terms: -0.722222222 + x = -0.474666874 Solving -0.722222222 + x = -0.474666874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = -0.474666874 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = -0.474666874 + 0.722222222 x = -0.474666874 + 0.722222222 Combine like terms: -0.474666874 + 0.722222222 = 0.247555348 x = 0.247555348 Simplifying x = 0.247555348Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.196889096, 0.247555348}
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