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Simplifying x2 + 8x + -22 = 0 Reorder the terms: -22 + 8x + x2 = 0 Solving -22 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 8x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 8x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 8x + x2 = 0 + 22 8x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 8x + x2 = 22 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 22 + 16 Reorder the terms: 16 + 8x + x2 = 22 + 16 Combine like terms: 22 + 16 = 38 16 + 8x + x2 = 38 Factor a perfect square on the left side: (x + 4)(x + 4) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + 4) equal to 6.164414003 and -6.164414003.Subproblem 1
x + 4 = 6.164414003 Simplifying x + 4 = 6.164414003 Reorder the terms: 4 + x = 6.164414003 Solving 4 + x = 6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6.164414003 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.164414003 + -4 x = 6.164414003 + -4 Combine like terms: 6.164414003 + -4 = 2.164414003 x = 2.164414003 Simplifying x = 2.164414003Subproblem 2
x + 4 = -6.164414003 Simplifying x + 4 = -6.164414003 Reorder the terms: 4 + x = -6.164414003 Solving 4 + x = -6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6.164414003 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.164414003 + -4 x = -6.164414003 + -4 Combine like terms: -6.164414003 + -4 = -10.164414003 x = -10.164414003 Simplifying x = -10.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.164414003, -10.164414003}
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