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Simplifying x2 + 22x + 19 = 0 Reorder the terms: 19 + 22x + x2 = 0 Solving 19 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 22x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 22x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 22x + x2 = 0 + -19 22x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 22x + x2 = -19 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 = -19 + 121 Reorder the terms: 121 + 22x + x2 = -19 + 121 Combine like terms: -19 + 121 = 102 121 + 22x + x2 = 102 Factor a perfect square on the left side: (x + 11)(x + 11) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (x + 11) equal to 10.099504938 and -10.099504938.Subproblem 1
x + 11 = 10.099504938 Simplifying x + 11 = 10.099504938 Reorder the terms: 11 + x = 10.099504938 Solving 11 + x = 10.099504938 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 = 10.099504938 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.099504938 + -11 x = 10.099504938 + -11 Combine like terms: 10.099504938 + -11 = -0.900495062 x = -0.900495062 Simplifying x = -0.900495062Subproblem 2
x + 11 = -10.099504938 Simplifying x + 11 = -10.099504938 Reorder the terms: 11 + x = -10.099504938 Solving 11 + x = -10.099504938 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 = -10.099504938 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.099504938 + -11 x = -10.099504938 + -11 Combine like terms: -10.099504938 + -11 = -21.099504938 x = -21.099504938 Simplifying x = -21.099504938Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.900495062, -21.099504938}
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