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Simplifying 27x2 + 5 = 42x Reorder the terms: 5 + 27x2 = 42x Solving 5 + 27x2 = 42x Solving for variable 'x'. Reorder the terms: 5 + -42x + 27x2 = 42x + -42x Combine like terms: 42x + -42x = 0 5 + -42x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.1851851852 + -1.555555556x + x2 = 0 Move the constant term to the right: Add '-0.1851851852' to each side of the equation. 0.1851851852 + -1.555555556x + -0.1851851852 + x2 = 0 + -0.1851851852 Reorder the terms: 0.1851851852 + -0.1851851852 + -1.555555556x + x2 = 0 + -0.1851851852 Combine like terms: 0.1851851852 + -0.1851851852 = 0.0000000000 0.0000000000 + -1.555555556x + x2 = 0 + -0.1851851852 -1.555555556x + x2 = 0 + -0.1851851852 Combine like terms: 0 + -0.1851851852 = -0.1851851852 -1.555555556x + x2 = -0.1851851852 The x term is -1.555555556x. Take half its coefficient (-0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. -1.555555556x + 0.6049382720 + x2 = -0.1851851852 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556x + x2 = -0.1851851852 + 0.6049382720 Combine like terms: -0.1851851852 + 0.6049382720 = 0.4197530868 0.6049382720 + -1.555555556x + x2 = 0.4197530868 Factor a perfect square on the left side: (x + -0.777777778)(x + -0.777777778) = 0.4197530868 Calculate the square root of the right side: 0.647883544 Break this problem into two subproblems by setting (x + -0.777777778) equal to 0.647883544 and -0.647883544.Subproblem 1
x + -0.777777778 = 0.647883544 Simplifying x + -0.777777778 = 0.647883544 Reorder the terms: -0.777777778 + x = 0.647883544 Solving -0.777777778 + x = 0.647883544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = 0.647883544 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 0.647883544 + 0.777777778 x = 0.647883544 + 0.777777778 Combine like terms: 0.647883544 + 0.777777778 = 1.425661322 x = 1.425661322 Simplifying x = 1.425661322Subproblem 2
x + -0.777777778 = -0.647883544 Simplifying x + -0.777777778 = -0.647883544 Reorder the terms: -0.777777778 + x = -0.647883544 Solving -0.777777778 + x = -0.647883544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = -0.647883544 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -0.647883544 + 0.777777778 x = -0.647883544 + 0.777777778 Combine like terms: -0.647883544 + 0.777777778 = 0.129894234 x = 0.129894234 Simplifying x = 0.129894234Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.425661322, 0.129894234}
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