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Simplifying x2 + 6x + -221 = 0 Reorder the terms: -221 + 6x + x2 = 0 Solving -221 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '221' to each side of the equation. -221 + 6x + 221 + x2 = 0 + 221 Reorder the terms: -221 + 221 + 6x + x2 = 0 + 221 Combine like terms: -221 + 221 = 0 0 + 6x + x2 = 0 + 221 6x + x2 = 0 + 221 Combine like terms: 0 + 221 = 221 6x + x2 = 221 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 221 + 9 Reorder the terms: 9 + 6x + x2 = 221 + 9 Combine like terms: 221 + 9 = 230 9 + 6x + x2 = 230 Factor a perfect square on the left side: (x + 3)(x + 3) = 230 Calculate the square root of the right side: 15.165750888 Break this problem into two subproblems by setting (x + 3) equal to 15.165750888 and -15.165750888.Subproblem 1
x + 3 = 15.165750888 Simplifying x + 3 = 15.165750888 Reorder the terms: 3 + x = 15.165750888 Solving 3 + x = 15.165750888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 15.165750888 + -3 Combine like terms: 3 + -3 = 0 0 + x = 15.165750888 + -3 x = 15.165750888 + -3 Combine like terms: 15.165750888 + -3 = 12.165750888 x = 12.165750888 Simplifying x = 12.165750888Subproblem 2
x + 3 = -15.165750888 Simplifying x + 3 = -15.165750888 Reorder the terms: 3 + x = -15.165750888 Solving 3 + x = -15.165750888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -15.165750888 + -3 Combine like terms: 3 + -3 = 0 0 + x = -15.165750888 + -3 x = -15.165750888 + -3 Combine like terms: -15.165750888 + -3 = -18.165750888 x = -18.165750888 Simplifying x = -18.165750888Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.165750888, -18.165750888}
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