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Simplifying 81x2 + 54x + 1 = 0 Reorder the terms: 1 + 54x + 81x2 = 0 Solving 1 + 54x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 0.01234567901 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.01234567901' to each side of the equation. 0.01234567901 + 0.6666666667x + -0.01234567901 + x2 = 0 + -0.01234567901 Reorder the terms: 0.01234567901 + -0.01234567901 + 0.6666666667x + x2 = 0 + -0.01234567901 Combine like terms: 0.01234567901 + -0.01234567901 = 0.00000000000 0.00000000000 + 0.6666666667x + x2 = 0 + -0.01234567901 0.6666666667x + x2 = 0 + -0.01234567901 Combine like terms: 0 + -0.01234567901 = -0.01234567901 0.6666666667x + x2 = -0.01234567901 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -0.01234567901 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.01234567901 + 0.1111111112 Combine like terms: -0.01234567901 + 0.1111111112 = 0.09876543219 0.1111111112 + 0.6666666667x + x2 = 0.09876543219 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.09876543219 Calculate the square root of the right side: 0.314269681 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.314269681 and -0.314269681.Subproblem 1
x + 0.3333333334 = 0.314269681 Simplifying x + 0.3333333334 = 0.314269681 Reorder the terms: 0.3333333334 + x = 0.314269681 Solving 0.3333333334 + x = 0.314269681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.314269681 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.314269681 + -0.3333333334 x = 0.314269681 + -0.3333333334 Combine like terms: 0.314269681 + -0.3333333334 = -0.0190636524 x = -0.0190636524 Simplifying x = -0.0190636524Subproblem 2
x + 0.3333333334 = -0.314269681 Simplifying x + 0.3333333334 = -0.314269681 Reorder the terms: 0.3333333334 + x = -0.314269681 Solving 0.3333333334 + x = -0.314269681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.314269681 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.314269681 + -0.3333333334 x = -0.314269681 + -0.3333333334 Combine like terms: -0.314269681 + -0.3333333334 = -0.6476030144 x = -0.6476030144 Simplifying x = -0.6476030144Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0190636524, -0.6476030144}
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