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Simplifying x2 + 18x = -3 Reorder the terms: 18x + x2 = -3 Solving 18x + x2 = -3 Solving for variable 'x'. Reorder the terms: 3 + 18x + x2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 18x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 18x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 18x + x2 = 0 + -3 18x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 18x + x2 = -3 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -3 + 81 Reorder the terms: 81 + 18x + x2 = -3 + 81 Combine like terms: -3 + 81 = 78 81 + 18x + x2 = 78 Factor a perfect square on the left side: (x + 9)(x + 9) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + 9) equal to 8.831760866 and -8.831760866.Subproblem 1
x + 9 = 8.831760866 Simplifying x + 9 = 8.831760866 Reorder the terms: 9 + x = 8.831760866 Solving 9 + x = 8.831760866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 8.831760866 + -9 Combine like terms: 9 + -9 = 0 0 + x = 8.831760866 + -9 x = 8.831760866 + -9 Combine like terms: 8.831760866 + -9 = -0.168239134 x = -0.168239134 Simplifying x = -0.168239134Subproblem 2
x + 9 = -8.831760866 Simplifying x + 9 = -8.831760866 Reorder the terms: 9 + x = -8.831760866 Solving 9 + x = -8.831760866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -8.831760866 + -9 Combine like terms: 9 + -9 = 0 0 + x = -8.831760866 + -9 x = -8.831760866 + -9 Combine like terms: -8.831760866 + -9 = -17.831760866 x = -17.831760866 Simplifying x = -17.831760866Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.168239134, -17.831760866}
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