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Simplifying 5.2x2 + 3.1x + -2.5 = 0 Reorder the terms: -2.5 + 3.1x + 5.2x2 = 0 Solving -2.5 + 3.1x + 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'. -0.4807692308 + 0.5961538462x + x2 = 0 Move the constant term to the right: Add '0.4807692308' to each side of the equation. -0.4807692308 + 0.5961538462x + 0.4807692308 + x2 = 0 + 0.4807692308 Reorder the terms: -0.4807692308 + 0.4807692308 + 0.5961538462x + x2 = 0 + 0.4807692308 Combine like terms: -0.4807692308 + 0.4807692308 = 0.0000000000 0.0000000000 + 0.5961538462x + x2 = 0 + 0.4807692308 0.5961538462x + x2 = 0 + 0.4807692308 Combine like terms: 0 + 0.4807692308 = 0.4807692308 0.5961538462x + x2 = 0.4807692308 The x term is 0.5961538462x. Take half its coefficient (0.2980769231). Square it (0.08884985208) and add it to both sides. Add '0.08884985208' to each side of the equation. 0.5961538462x + 0.08884985208 + x2 = 0.4807692308 + 0.08884985208 Reorder the terms: 0.08884985208 + 0.5961538462x + x2 = 0.4807692308 + 0.08884985208 Combine like terms: 0.4807692308 + 0.08884985208 = 0.56961908288 0.08884985208 + 0.5961538462x + x2 = 0.56961908288 Factor a perfect square on the left side: (x + 0.2980769231)(x + 0.2980769231) = 0.56961908288 Calculate the square root of the right side: 0.754731133 Break this problem into two subproblems by setting (x + 0.2980769231) equal to 0.754731133 and -0.754731133.Subproblem 1
x + 0.2980769231 = 0.754731133 Simplifying x + 0.2980769231 = 0.754731133 Reorder the terms: 0.2980769231 + x = 0.754731133 Solving 0.2980769231 + x = 0.754731133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2980769231' to each side of the equation. 0.2980769231 + -0.2980769231 + x = 0.754731133 + -0.2980769231 Combine like terms: 0.2980769231 + -0.2980769231 = 0.0000000000 0.0000000000 + x = 0.754731133 + -0.2980769231 x = 0.754731133 + -0.2980769231 Combine like terms: 0.754731133 + -0.2980769231 = 0.4566542099 x = 0.4566542099 Simplifying x = 0.4566542099Subproblem 2
x + 0.2980769231 = -0.754731133 Simplifying x + 0.2980769231 = -0.754731133 Reorder the terms: 0.2980769231 + x = -0.754731133 Solving 0.2980769231 + x = -0.754731133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2980769231' to each side of the equation. 0.2980769231 + -0.2980769231 + x = -0.754731133 + -0.2980769231 Combine like terms: 0.2980769231 + -0.2980769231 = 0.0000000000 0.0000000000 + x = -0.754731133 + -0.2980769231 x = -0.754731133 + -0.2980769231 Combine like terms: -0.754731133 + -0.2980769231 = -1.0528080561 x = -1.0528080561 Simplifying x = -1.0528080561Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4566542099, -1.0528080561}
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