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Simplifying x2 + 20x = -22 Reorder the terms: 20x + x2 = -22 Solving 20x + x2 = -22 Solving for variable 'x'. Reorder the terms: 22 + 20x + x2 = -22 + 22 Combine like terms: -22 + 22 = 0 22 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 20x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + 20x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 20x + x2 = 0 + -22 20x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 20x + x2 = -22 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -22 + 100 Reorder the terms: 100 + 20x + x2 = -22 + 100 Combine like terms: -22 + 100 = 78 100 + 20x + x2 = 78 Factor a perfect square on the left side: (x + 10)(x + 10) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + 10) equal to 8.831760866 and -8.831760866.Subproblem 1
x + 10 = 8.831760866 Simplifying x + 10 = 8.831760866 Reorder the terms: 10 + x = 8.831760866 Solving 10 + x = 8.831760866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 8.831760866 + -10 Combine like terms: 10 + -10 = 0 0 + x = 8.831760866 + -10 x = 8.831760866 + -10 Combine like terms: 8.831760866 + -10 = -1.168239134 x = -1.168239134 Simplifying x = -1.168239134Subproblem 2
x + 10 = -8.831760866 Simplifying x + 10 = -8.831760866 Reorder the terms: 10 + x = -8.831760866 Solving 10 + x = -8.831760866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -8.831760866 + -10 Combine like terms: 10 + -10 = 0 0 + x = -8.831760866 + -10 x = -8.831760866 + -10 Combine like terms: -8.831760866 + -10 = -18.831760866 x = -18.831760866 Simplifying x = -18.831760866Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.168239134, -18.831760866}
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