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Simplifying 0 = x2 + 16x + -22 Reorder the terms: 0 = -22 + 16x + x2 Solving 0 = -22 + 16x + x2 Solving for variable 'x'. Combine like terms: 0 + 22 = 22 22 + -16x + -1x2 = -22 + 16x + x2 + 22 + -16x + -1x2 Reorder the terms: 22 + -16x + -1x2 = -22 + 22 + 16x + -16x + x2 + -1x2 Combine like terms: -22 + 22 = 0 22 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2 22 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 22 + -16x + -1x2 = 0 + x2 + -1x2 22 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 22 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -22 + 16x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 16x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 16x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 16x + x2 = 0 + 22 16x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 16x + x2 = 22 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 22 + 64 Reorder the terms: 64 + 16x + x2 = 22 + 64 Combine like terms: 22 + 64 = 86 64 + 16x + x2 = 86 Factor a perfect square on the left side: (x + 8)(x + 8) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + 8) equal to 9.273618495 and -9.273618495.Subproblem 1
x + 8 = 9.273618495 Simplifying x + 8 = 9.273618495 Reorder the terms: 8 + x = 9.273618495 Solving 8 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 9.273618495 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.273618495 + -8 x = 9.273618495 + -8 Combine like terms: 9.273618495 + -8 = 1.273618495 x = 1.273618495 Simplifying x = 1.273618495Subproblem 2
x + 8 = -9.273618495 Simplifying x + 8 = -9.273618495 Reorder the terms: 8 + x = -9.273618495 Solving 8 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -9.273618495 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.273618495 + -8 x = -9.273618495 + -8 Combine like terms: -9.273618495 + -8 = -17.273618495 x = -17.273618495 Simplifying x = -17.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.273618495, -17.273618495}
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