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Simplifying x2 + 30x + 11 = 0 Reorder the terms: 11 + 30x + x2 = 0 Solving 11 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 30x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 30x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 30x + x2 = 0 + -11 30x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 30x + x2 = -11 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -11 + 225 Reorder the terms: 225 + 30x + x2 = -11 + 225 Combine like terms: -11 + 225 = 214 225 + 30x + x2 = 214 Factor a perfect square on the left side: (x + 15)(x + 15) = 214 Calculate the square root of the right side: 14.628738838 Break this problem into two subproblems by setting (x + 15) equal to 14.628738838 and -14.628738838.Subproblem 1
x + 15 = 14.628738838 Simplifying x + 15 = 14.628738838 Reorder the terms: 15 + x = 14.628738838 Solving 15 + x = 14.628738838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 14.628738838 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.628738838 + -15 x = 14.628738838 + -15 Combine like terms: 14.628738838 + -15 = -0.371261162 x = -0.371261162 Simplifying x = -0.371261162Subproblem 2
x + 15 = -14.628738838 Simplifying x + 15 = -14.628738838 Reorder the terms: 15 + x = -14.628738838 Solving 15 + x = -14.628738838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -14.628738838 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.628738838 + -15 x = -14.628738838 + -15 Combine like terms: -14.628738838 + -15 = -29.628738838 x = -29.628738838 Simplifying x = -29.628738838Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.371261162, -29.628738838}
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