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Simplifying 162x2 + 36x + 1 = 0 Reorder the terms: 1 + 36x + 162x2 = 0 Solving 1 + 36x + 162x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 162 the coefficient of the squared term: Divide each side by '162'. 0.006172839506 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '-0.006172839506' to each side of the equation. 0.006172839506 + 0.2222222222x + -0.006172839506 + x2 = 0 + -0.006172839506 Reorder the terms: 0.006172839506 + -0.006172839506 + 0.2222222222x + x2 = 0 + -0.006172839506 Combine like terms: 0.006172839506 + -0.006172839506 = 0.000000000000 0.000000000000 + 0.2222222222x + x2 = 0 + -0.006172839506 0.2222222222x + x2 = 0 + -0.006172839506 Combine like terms: 0 + -0.006172839506 = -0.006172839506 0.2222222222x + x2 = -0.006172839506 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = -0.006172839506 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = -0.006172839506 + 0.01234567901 Combine like terms: -0.006172839506 + 0.01234567901 = 0.006172839504 0.01234567901 + 0.2222222222x + x2 = 0.006172839504 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 0.006172839504 Calculate the square root of the right side: 0.07856742 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 0.07856742 and -0.07856742.Subproblem 1
x + 0.1111111111 = 0.07856742 Simplifying x + 0.1111111111 = 0.07856742 Reorder the terms: 0.1111111111 + x = 0.07856742 Solving 0.1111111111 + x = 0.07856742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 0.07856742 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.07856742 + -0.1111111111 x = 0.07856742 + -0.1111111111 Combine like terms: 0.07856742 + -0.1111111111 = -0.0325436911 x = -0.0325436911 Simplifying x = -0.0325436911Subproblem 2
x + 0.1111111111 = -0.07856742 Simplifying x + 0.1111111111 = -0.07856742 Reorder the terms: 0.1111111111 + x = -0.07856742 Solving 0.1111111111 + x = -0.07856742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -0.07856742 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.07856742 + -0.1111111111 x = -0.07856742 + -0.1111111111 Combine like terms: -0.07856742 + -0.1111111111 = -0.1896785311 x = -0.1896785311 Simplifying x = -0.1896785311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0325436911, -0.1896785311}
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