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Simplifying 361x2 + 76x + 2 = 0 Reorder the terms: 2 + 76x + 361x2 = 0 Solving 2 + 76x + 361x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 361 the coefficient of the squared term: Divide each side by '361'. 0.005540166205 + 0.2105263158x + x2 = 0 Move the constant term to the right: Add '-0.005540166205' to each side of the equation. 0.005540166205 + 0.2105263158x + -0.005540166205 + x2 = 0 + -0.005540166205 Reorder the terms: 0.005540166205 + -0.005540166205 + 0.2105263158x + x2 = 0 + -0.005540166205 Combine like terms: 0.005540166205 + -0.005540166205 = 0.000000000000 0.000000000000 + 0.2105263158x + x2 = 0 + -0.005540166205 0.2105263158x + x2 = 0 + -0.005540166205 Combine like terms: 0 + -0.005540166205 = -0.005540166205 0.2105263158x + x2 = -0.005540166205 The x term is 0.2105263158x. Take half its coefficient (0.1052631579). Square it (0.01108033241) and add it to both sides. Add '0.01108033241' to each side of the equation. 0.2105263158x + 0.01108033241 + x2 = -0.005540166205 + 0.01108033241 Reorder the terms: 0.01108033241 + 0.2105263158x + x2 = -0.005540166205 + 0.01108033241 Combine like terms: -0.005540166205 + 0.01108033241 = 0.005540166205 0.01108033241 + 0.2105263158x + x2 = 0.005540166205 Factor a perfect square on the left side: (x + 0.1052631579)(x + 0.1052631579) = 0.005540166205 Calculate the square root of the right side: 0.074432293 Break this problem into two subproblems by setting (x + 0.1052631579) equal to 0.074432293 and -0.074432293.Subproblem 1
x + 0.1052631579 = 0.074432293 Simplifying x + 0.1052631579 = 0.074432293 Reorder the terms: 0.1052631579 + x = 0.074432293 Solving 0.1052631579 + x = 0.074432293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1052631579' to each side of the equation. 0.1052631579 + -0.1052631579 + x = 0.074432293 + -0.1052631579 Combine like terms: 0.1052631579 + -0.1052631579 = 0.0000000000 0.0000000000 + x = 0.074432293 + -0.1052631579 x = 0.074432293 + -0.1052631579 Combine like terms: 0.074432293 + -0.1052631579 = -0.0308308649 x = -0.0308308649 Simplifying x = -0.0308308649Subproblem 2
x + 0.1052631579 = -0.074432293 Simplifying x + 0.1052631579 = -0.074432293 Reorder the terms: 0.1052631579 + x = -0.074432293 Solving 0.1052631579 + x = -0.074432293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1052631579' to each side of the equation. 0.1052631579 + -0.1052631579 + x = -0.074432293 + -0.1052631579 Combine like terms: 0.1052631579 + -0.1052631579 = 0.0000000000 0.0000000000 + x = -0.074432293 + -0.1052631579 x = -0.074432293 + -0.1052631579 Combine like terms: -0.074432293 + -0.1052631579 = -0.1796954509 x = -0.1796954509 Simplifying x = -0.1796954509Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0308308649, -0.1796954509}
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