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Simplifying x2 + 30x + 23 = 0 Reorder the terms: 23 + 30x + x2 = 0 Solving 23 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + 30x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + 30x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 30x + x2 = 0 + -23 30x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 30x + x2 = -23 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 = -23 + 225 Reorder the terms: 225 + 30x + x2 = -23 + 225 Combine like terms: -23 + 225 = 202 225 + 30x + x2 = 202 Factor a perfect square on the left side: (x + 15)(x + 15) = 202 Calculate the square root of the right side: 14.212670404 Break this problem into two subproblems by setting (x + 15) equal to 14.212670404 and -14.212670404.Subproblem 1
x + 15 = 14.212670404 Simplifying x + 15 = 14.212670404 Reorder the terms: 15 + x = 14.212670404 Solving 15 + x = 14.212670404 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 = 14.212670404 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.212670404 + -15 x = 14.212670404 + -15 Combine like terms: 14.212670404 + -15 = -0.787329596 x = -0.787329596 Simplifying x = -0.787329596Subproblem 2
x + 15 = -14.212670404 Simplifying x + 15 = -14.212670404 Reorder the terms: 15 + x = -14.212670404 Solving 15 + x = -14.212670404 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 = -14.212670404 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.212670404 + -15 x = -14.212670404 + -15 Combine like terms: -14.212670404 + -15 = -29.212670404 x = -29.212670404 Simplifying x = -29.212670404Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.787329596, -29.212670404}
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