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Simplifying x2 + 30x + -221 = 0 Reorder the terms: -221 + 30x + x2 = 0 Solving -221 + 30x + 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 + 30x + 221 + x2 = 0 + 221 Reorder the terms: -221 + 221 + 30x + x2 = 0 + 221 Combine like terms: -221 + 221 = 0 0 + 30x + x2 = 0 + 221 30x + x2 = 0 + 221 Combine like terms: 0 + 221 = 221 30x + x2 = 221 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 = 221 + 225 Reorder the terms: 225 + 30x + x2 = 221 + 225 Combine like terms: 221 + 225 = 446 225 + 30x + x2 = 446 Factor a perfect square on the left side: (x + 15)(x + 15) = 446 Calculate the square root of the right side: 21.118712082 Break this problem into two subproblems by setting (x + 15) equal to 21.118712082 and -21.118712082.Subproblem 1
x + 15 = 21.118712082 Simplifying x + 15 = 21.118712082 Reorder the terms: 15 + x = 21.118712082 Solving 15 + x = 21.118712082 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 = 21.118712082 + -15 Combine like terms: 15 + -15 = 0 0 + x = 21.118712082 + -15 x = 21.118712082 + -15 Combine like terms: 21.118712082 + -15 = 6.118712082 x = 6.118712082 Simplifying x = 6.118712082Subproblem 2
x + 15 = -21.118712082 Simplifying x + 15 = -21.118712082 Reorder the terms: 15 + x = -21.118712082 Solving 15 + x = -21.118712082 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 = -21.118712082 + -15 Combine like terms: 15 + -15 = 0 0 + x = -21.118712082 + -15 x = -21.118712082 + -15 Combine like terms: -21.118712082 + -15 = -36.118712082 x = -36.118712082 Simplifying x = -36.118712082Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.118712082, -36.118712082}
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