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Simplifying 0.61 + 8.5x + 4.9x2 = 0 Solving 0.61 + 8.5x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.1244897959 + 1.734693878x + x2 = 0 Move the constant term to the right: Add '-0.1244897959' to each side of the equation. 0.1244897959 + 1.734693878x + -0.1244897959 + x2 = 0 + -0.1244897959 Reorder the terms: 0.1244897959 + -0.1244897959 + 1.734693878x + x2 = 0 + -0.1244897959 Combine like terms: 0.1244897959 + -0.1244897959 = 0.0000000000 0.0000000000 + 1.734693878x + x2 = 0 + -0.1244897959 1.734693878x + x2 = 0 + -0.1244897959 Combine like terms: 0 + -0.1244897959 = -0.1244897959 1.734693878x + x2 = -0.1244897959 The x term is 1.734693878x. Take half its coefficient (0.867346939). Square it (0.7522907126) and add it to both sides. Add '0.7522907126' to each side of the equation. 1.734693878x + 0.7522907126 + x2 = -0.1244897959 + 0.7522907126 Reorder the terms: 0.7522907126 + 1.734693878x + x2 = -0.1244897959 + 0.7522907126 Combine like terms: -0.1244897959 + 0.7522907126 = 0.6278009167 0.7522907126 + 1.734693878x + x2 = 0.6278009167 Factor a perfect square on the left side: (x + 0.867346939)(x + 0.867346939) = 0.6278009167 Calculate the square root of the right side: 0.79233889 Break this problem into two subproblems by setting (x + 0.867346939) equal to 0.79233889 and -0.79233889.Subproblem 1
x + 0.867346939 = 0.79233889 Simplifying x + 0.867346939 = 0.79233889 Reorder the terms: 0.867346939 + x = 0.79233889 Solving 0.867346939 + x = 0.79233889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.867346939' to each side of the equation. 0.867346939 + -0.867346939 + x = 0.79233889 + -0.867346939 Combine like terms: 0.867346939 + -0.867346939 = 0.000000000 0.000000000 + x = 0.79233889 + -0.867346939 x = 0.79233889 + -0.867346939 Combine like terms: 0.79233889 + -0.867346939 = -0.075008049 x = -0.075008049 Simplifying x = -0.075008049Subproblem 2
x + 0.867346939 = -0.79233889 Simplifying x + 0.867346939 = -0.79233889 Reorder the terms: 0.867346939 + x = -0.79233889 Solving 0.867346939 + x = -0.79233889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.867346939' to each side of the equation. 0.867346939 + -0.867346939 + x = -0.79233889 + -0.867346939 Combine like terms: 0.867346939 + -0.867346939 = 0.000000000 0.000000000 + x = -0.79233889 + -0.867346939 x = -0.79233889 + -0.867346939 Combine like terms: -0.79233889 + -0.867346939 = -1.659685829 x = -1.659685829 Simplifying x = -1.659685829Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.075008049, -1.659685829}
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