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Simplifying x2 + 22x + 33 = 0 Reorder the terms: 33 + 22x + x2 = 0 Solving 33 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + 22x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + 22x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 22x + x2 = 0 + -33 22x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 22x + x2 = -33 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -33 + 121 Reorder the terms: 121 + 22x + x2 = -33 + 121 Combine like terms: -33 + 121 = 88 121 + 22x + x2 = 88 Factor a perfect square on the left side: (x + 11)(x + 11) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + 11) equal to 9.38083152 and -9.38083152.Subproblem 1
x + 11 = 9.38083152 Simplifying x + 11 = 9.38083152 Reorder the terms: 11 + x = 9.38083152 Solving 11 + x = 9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 9.38083152 + -11 Combine like terms: 11 + -11 = 0 0 + x = 9.38083152 + -11 x = 9.38083152 + -11 Combine like terms: 9.38083152 + -11 = -1.61916848 x = -1.61916848 Simplifying x = -1.61916848Subproblem 2
x + 11 = -9.38083152 Simplifying x + 11 = -9.38083152 Reorder the terms: 11 + x = -9.38083152 Solving 11 + x = -9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -9.38083152 + -11 Combine like terms: 11 + -11 = 0 0 + x = -9.38083152 + -11 x = -9.38083152 + -11 Combine like terms: -9.38083152 + -11 = -20.38083152 x = -20.38083152 Simplifying x = -20.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.61916848, -20.38083152}
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