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Simplifying 30x2 + -27x + 2 = 0 Reorder the terms: 2 + -27x + 30x2 = 0 Solving 2 + -27x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.06666666667 + -0.9x + x2 = 0 Move the constant term to the right: Add '-0.06666666667' to each side of the equation. 0.06666666667 + -0.9x + -0.06666666667 + x2 = 0 + -0.06666666667 Reorder the terms: 0.06666666667 + -0.06666666667 + -0.9x + x2 = 0 + -0.06666666667 Combine like terms: 0.06666666667 + -0.06666666667 = 0.00000000000 0.00000000000 + -0.9x + x2 = 0 + -0.06666666667 -0.9x + x2 = 0 + -0.06666666667 Combine like terms: 0 + -0.06666666667 = -0.06666666667 -0.9x + x2 = -0.06666666667 The x term is -0.9x. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x + 0.2025 + x2 = -0.06666666667 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = -0.06666666667 + 0.2025 Combine like terms: -0.06666666667 + 0.2025 = 0.13583333333 0.2025 + -0.9x + x2 = 0.13583333333 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = 0.13583333333 Calculate the square root of the right side: 0.36855574 Break this problem into two subproblems by setting (x + -0.45) equal to 0.36855574 and -0.36855574.Subproblem 1
x + -0.45 = 0.36855574 Simplifying x + -0.45 = 0.36855574 Reorder the terms: -0.45 + x = 0.36855574 Solving -0.45 + x = 0.36855574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 0.36855574 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 0.36855574 + 0.45 x = 0.36855574 + 0.45 Combine like terms: 0.36855574 + 0.45 = 0.81855574 x = 0.81855574 Simplifying x = 0.81855574Subproblem 2
x + -0.45 = -0.36855574 Simplifying x + -0.45 = -0.36855574 Reorder the terms: -0.45 + x = -0.36855574 Solving -0.45 + x = -0.36855574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -0.36855574 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -0.36855574 + 0.45 x = -0.36855574 + 0.45 Combine like terms: -0.36855574 + 0.45 = 0.08144426 x = 0.08144426 Simplifying x = 0.08144426Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.81855574, 0.08144426}
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