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Simplifying x2 + 3.98x + -0.05057 = 0 Reorder the terms: -0.05057 + 3.98x + x2 = 0 Solving -0.05057 + 3.98x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.05057' to each side of the equation. -0.05057 + 3.98x + 0.05057 + x2 = 0 + 0.05057 Reorder the terms: -0.05057 + 0.05057 + 3.98x + x2 = 0 + 0.05057 Combine like terms: -0.05057 + 0.05057 = 0.00000 0.00000 + 3.98x + x2 = 0 + 0.05057 3.98x + x2 = 0 + 0.05057 Combine like terms: 0 + 0.05057 = 0.05057 3.98x + x2 = 0.05057 The x term is 3.98x. Take half its coefficient (1.99). Square it (3.9601) and add it to both sides. Add '3.9601' to each side of the equation. 3.98x + 3.9601 + x2 = 0.05057 + 3.9601 Reorder the terms: 3.9601 + 3.98x + x2 = 0.05057 + 3.9601 Combine like terms: 0.05057 + 3.9601 = 4.01067 3.9601 + 3.98x + x2 = 4.01067 Factor a perfect square on the left side: (x + 1.99)(x + 1.99) = 4.01067 Calculate the square root of the right side: 2.002665723 Break this problem into two subproblems by setting (x + 1.99) equal to 2.002665723 and -2.002665723.Subproblem 1
x + 1.99 = 2.002665723 Simplifying x + 1.99 = 2.002665723 Reorder the terms: 1.99 + x = 2.002665723 Solving 1.99 + x = 2.002665723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.99' to each side of the equation. 1.99 + -1.99 + x = 2.002665723 + -1.99 Combine like terms: 1.99 + -1.99 = 0.00 0.00 + x = 2.002665723 + -1.99 x = 2.002665723 + -1.99 Combine like terms: 2.002665723 + -1.99 = 0.012665723 x = 0.012665723 Simplifying x = 0.012665723Subproblem 2
x + 1.99 = -2.002665723 Simplifying x + 1.99 = -2.002665723 Reorder the terms: 1.99 + x = -2.002665723 Solving 1.99 + x = -2.002665723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.99' to each side of the equation. 1.99 + -1.99 + x = -2.002665723 + -1.99 Combine like terms: 1.99 + -1.99 = 0.00 0.00 + x = -2.002665723 + -1.99 x = -2.002665723 + -1.99 Combine like terms: -2.002665723 + -1.99 = -3.992665723 x = -3.992665723 Simplifying x = -3.992665723Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.012665723, -3.992665723}
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