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Simplifying x2 = 19 + -11x Solving x2 = 19 + -11x Solving for variable 'x'. Reorder the terms: -19 + 11x + x2 = 19 + -11x + -19 + 11x Reorder the terms: -19 + 11x + x2 = 19 + -19 + -11x + 11x Combine like terms: 19 + -19 = 0 -19 + 11x + x2 = 0 + -11x + 11x -19 + 11x + x2 = -11x + 11x Combine like terms: -11x + 11x = 0 -19 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 11x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 11x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 11x + x2 = 0 + 19 11x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 11x + x2 = 19 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 19 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 19 + 30.25 Combine like terms: 19 + 30.25 = 49.25 30.25 + 11x + x2 = 49.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + 5.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + 5.5 = 7.017834424 Simplifying x + 5.5 = 7.017834424 Reorder the terms: 5.5 + x = 7.017834424 Solving 5.5 + x = 7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 7.017834424 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.017834424 + -5.5 x = 7.017834424 + -5.5 Combine like terms: 7.017834424 + -5.5 = 1.517834424 x = 1.517834424 Simplifying x = 1.517834424Subproblem 2
x + 5.5 = -7.017834424 Simplifying x + 5.5 = -7.017834424 Reorder the terms: 5.5 + x = -7.017834424 Solving 5.5 + x = -7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -7.017834424 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.017834424 + -5.5 x = -7.017834424 + -5.5 Combine like terms: -7.017834424 + -5.5 = -12.517834424 x = -12.517834424 Simplifying x = -12.517834424Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.517834424, -12.517834424}
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