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Simplifying 5x2 + -11x + 5 = 0 Reorder the terms: 5 + -11x + 5x2 = 0 Solving 5 + -11x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + -2.2x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.2x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.2x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.2x + x2 = 0 + -1 -2.2x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.2x + x2 = -1 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = -1 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = -1 + 1.21 Combine like terms: -1 + 1.21 = 0.21 1.21 + -2.2x + x2 = 0.21 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 0.21 Calculate the square root of the right side: 0.458257569 Break this problem into two subproblems by setting (x + -1.1) equal to 0.458257569 and -0.458257569.Subproblem 1
x + -1.1 = 0.458257569 Simplifying x + -1.1 = 0.458257569 Reorder the terms: -1.1 + x = 0.458257569 Solving -1.1 + x = 0.458257569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 0.458257569 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 0.458257569 + 1.1 x = 0.458257569 + 1.1 Combine like terms: 0.458257569 + 1.1 = 1.558257569 x = 1.558257569 Simplifying x = 1.558257569Subproblem 2
x + -1.1 = -0.458257569 Simplifying x + -1.1 = -0.458257569 Reorder the terms: -1.1 + x = -0.458257569 Solving -1.1 + x = -0.458257569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -0.458257569 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -0.458257569 + 1.1 x = -0.458257569 + 1.1 Combine like terms: -0.458257569 + 1.1 = 0.641742431 x = 0.641742431 Simplifying x = 0.641742431Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.558257569, 0.641742431}
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