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Simplifying x2 + 30x + 6 = 0 Reorder the terms: 6 + 30x + x2 = 0 Solving 6 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 30x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 30x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 30x + x2 = 0 + -6 30x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 30x + x2 = -6 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 = -6 + 225 Reorder the terms: 225 + 30x + x2 = -6 + 225 Combine like terms: -6 + 225 = 219 225 + 30x + x2 = 219 Factor a perfect square on the left side: (x + 15)(x + 15) = 219 Calculate the square root of the right side: 14.798648587 Break this problem into two subproblems by setting (x + 15) equal to 14.798648587 and -14.798648587.Subproblem 1
x + 15 = 14.798648587 Simplifying x + 15 = 14.798648587 Reorder the terms: 15 + x = 14.798648587 Solving 15 + x = 14.798648587 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 = 14.798648587 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.798648587 + -15 x = 14.798648587 + -15 Combine like terms: 14.798648587 + -15 = -0.201351413 x = -0.201351413 Simplifying x = -0.201351413Subproblem 2
x + 15 = -14.798648587 Simplifying x + 15 = -14.798648587 Reorder the terms: 15 + x = -14.798648587 Solving 15 + x = -14.798648587 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 = -14.798648587 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.798648587 + -15 x = -14.798648587 + -15 Combine like terms: -14.798648587 + -15 = -29.798648587 x = -29.798648587 Simplifying x = -29.798648587Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.201351413, -29.798648587}
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