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Simplifying x2 + 30x + 171 = 0 Reorder the terms: 171 + 30x + x2 = 0 Solving 171 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-171' to each side of the equation. 171 + 30x + -171 + x2 = 0 + -171 Reorder the terms: 171 + -171 + 30x + x2 = 0 + -171 Combine like terms: 171 + -171 = 0 0 + 30x + x2 = 0 + -171 30x + x2 = 0 + -171 Combine like terms: 0 + -171 = -171 30x + x2 = -171 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 = -171 + 225 Reorder the terms: 225 + 30x + x2 = -171 + 225 Combine like terms: -171 + 225 = 54 225 + 30x + x2 = 54 Factor a perfect square on the left side: (x + 15)(x + 15) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + 15) equal to 7.348469228 and -7.348469228.Subproblem 1
x + 15 = 7.348469228 Simplifying x + 15 = 7.348469228 Reorder the terms: 15 + x = 7.348469228 Solving 15 + x = 7.348469228 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 = 7.348469228 + -15 Combine like terms: 15 + -15 = 0 0 + x = 7.348469228 + -15 x = 7.348469228 + -15 Combine like terms: 7.348469228 + -15 = -7.651530772 x = -7.651530772 Simplifying x = -7.651530772Subproblem 2
x + 15 = -7.348469228 Simplifying x + 15 = -7.348469228 Reorder the terms: 15 + x = -7.348469228 Solving 15 + x = -7.348469228 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 = -7.348469228 + -15 Combine like terms: 15 + -15 = 0 0 + x = -7.348469228 + -15 x = -7.348469228 + -15 Combine like terms: -7.348469228 + -15 = -22.348469228 x = -22.348469228 Simplifying x = -22.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.651530772, -22.348469228}
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