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Simplifying 56x2 + 49x + -1 = 0 Reorder the terms: -1 + 49x + 56x2 = 0 Solving -1 + 49x + 56x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. -0.01785714286 + 0.875x + x2 = 0 Move the constant term to the right: Add '0.01785714286' to each side of the equation. -0.01785714286 + 0.875x + 0.01785714286 + x2 = 0 + 0.01785714286 Reorder the terms: -0.01785714286 + 0.01785714286 + 0.875x + x2 = 0 + 0.01785714286 Combine like terms: -0.01785714286 + 0.01785714286 = 0.00000000000 0.00000000000 + 0.875x + x2 = 0 + 0.01785714286 0.875x + x2 = 0 + 0.01785714286 Combine like terms: 0 + 0.01785714286 = 0.01785714286 0.875x + x2 = 0.01785714286 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = 0.01785714286 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = 0.01785714286 + 0.19140625 Combine like terms: 0.01785714286 + 0.19140625 = 0.20926339286 0.19140625 + 0.875x + x2 = 0.20926339286 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 0.20926339286 Calculate the square root of the right side: 0.457453159 Break this problem into two subproblems by setting (x + 0.4375) equal to 0.457453159 and -0.457453159.Subproblem 1
x + 0.4375 = 0.457453159 Simplifying x + 0.4375 = 0.457453159 Reorder the terms: 0.4375 + x = 0.457453159 Solving 0.4375 + x = 0.457453159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 0.457453159 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 0.457453159 + -0.4375 x = 0.457453159 + -0.4375 Combine like terms: 0.457453159 + -0.4375 = 0.019953159 x = 0.019953159 Simplifying x = 0.019953159Subproblem 2
x + 0.4375 = -0.457453159 Simplifying x + 0.4375 = -0.457453159 Reorder the terms: 0.4375 + x = -0.457453159 Solving 0.4375 + x = -0.457453159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -0.457453159 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -0.457453159 + -0.4375 x = -0.457453159 + -0.4375 Combine like terms: -0.457453159 + -0.4375 = -0.894953159 x = -0.894953159 Simplifying x = -0.894953159Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.019953159, -0.894953159}
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