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Simplifying 5.2x2 + x + -1 = 0 Reorder the terms: -1 + x + 5.2x2 = 0 Solving -1 + x + 5.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.2 the coefficient of the squared term: Divide each side by '5.2'. -0.1923076923 + 0.1923076923x + x2 = 0 Move the constant term to the right: Add '0.1923076923' to each side of the equation. -0.1923076923 + 0.1923076923x + 0.1923076923 + x2 = 0 + 0.1923076923 Reorder the terms: -0.1923076923 + 0.1923076923 + 0.1923076923x + x2 = 0 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + 0.1923076923x + x2 = 0 + 0.1923076923 0.1923076923x + x2 = 0 + 0.1923076923 Combine like terms: 0 + 0.1923076923 = 0.1923076923 0.1923076923x + x2 = 0.1923076923 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1923076923x + 0.25 + x2 = 0.1923076923 + 0.25 Reorder the terms: 0.25 + 0.1923076923x + x2 = 0.1923076923 + 0.25 Combine like terms: 0.1923076923 + 0.25 = 0.4423076923 0.25 + 0.1923076923x + x2 = 0.4423076923 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.4423076923 Calculate the square root of the right side: 0.665062172 Break this problem into two subproblems by setting (x + 0.5) equal to 0.665062172 and -0.665062172.Subproblem 1
x + 0.5 = 0.665062172 Simplifying x + 0.5 = 0.665062172 Reorder the terms: 0.5 + x = 0.665062172 Solving 0.5 + x = 0.665062172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.665062172 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.665062172 + -0.5 x = 0.665062172 + -0.5 Combine like terms: 0.665062172 + -0.5 = 0.165062172 x = 0.165062172 Simplifying x = 0.165062172Subproblem 2
x + 0.5 = -0.665062172 Simplifying x + 0.5 = -0.665062172 Reorder the terms: 0.5 + x = -0.665062172 Solving 0.5 + x = -0.665062172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.665062172 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.665062172 + -0.5 x = -0.665062172 + -0.5 Combine like terms: -0.665062172 + -0.5 = -1.165062172 x = -1.165062172 Simplifying x = -1.165062172Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.165062172, -1.165062172}
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