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Simplifying x2 + 18x + 21 = 0 Reorder the terms: 21 + 18x + x2 = 0 Solving 21 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 18x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 18x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 18x + x2 = 0 + -21 18x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 18x + x2 = -21 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 = -21 + 81 Reorder the terms: 81 + 18x + x2 = -21 + 81 Combine like terms: -21 + 81 = 60 81 + 18x + x2 = 60 Factor a perfect square on the left side: (x + 9)(x + 9) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + 9) equal to 7.745966692 and -7.745966692.Subproblem 1
x + 9 = 7.745966692 Simplifying x + 9 = 7.745966692 Reorder the terms: 9 + x = 7.745966692 Solving 9 + x = 7.745966692 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 = 7.745966692 + -9 Combine like terms: 9 + -9 = 0 0 + x = 7.745966692 + -9 x = 7.745966692 + -9 Combine like terms: 7.745966692 + -9 = -1.254033308 x = -1.254033308 Simplifying x = -1.254033308Subproblem 2
x + 9 = -7.745966692 Simplifying x + 9 = -7.745966692 Reorder the terms: 9 + x = -7.745966692 Solving 9 + x = -7.745966692 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 = -7.745966692 + -9 Combine like terms: 9 + -9 = 0 0 + x = -7.745966692 + -9 x = -7.745966692 + -9 Combine like terms: -7.745966692 + -9 = -16.745966692 x = -16.745966692 Simplifying x = -16.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.254033308, -16.745966692}
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