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Simplifying x2 + -16x + 22 = 1 Reorder the terms: 22 + -16x + x2 = 1 Solving 22 + -16x + x2 = 1 Solving for variable 'x'. Reorder the terms: 22 + -1 + -16x + x2 = 1 + -1 Combine like terms: 22 + -1 = 21 21 + -16x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 21 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -16x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -16x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -16x + x2 = 0 + -21 -16x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -16x + x2 = -21 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 = -21 + 64 Reorder the terms: 64 + -16x + x2 = -21 + 64 Combine like terms: -21 + 64 = 43 64 + -16x + x2 = 43 Factor a perfect square on the left side: (x + -8)(x + -8) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + -8) equal to 6.557438524 and -6.557438524.Subproblem 1
x + -8 = 6.557438524 Simplifying x + -8 = 6.557438524 Reorder the terms: -8 + x = 6.557438524 Solving -8 + x = 6.557438524 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 = 6.557438524 + 8 Combine like terms: -8 + 8 = 0 0 + x = 6.557438524 + 8 x = 6.557438524 + 8 Combine like terms: 6.557438524 + 8 = 14.557438524 x = 14.557438524 Simplifying x = 14.557438524Subproblem 2
x + -8 = -6.557438524 Simplifying x + -8 = -6.557438524 Reorder the terms: -8 + x = -6.557438524 Solving -8 + x = -6.557438524 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 = -6.557438524 + 8 Combine like terms: -8 + 8 = 0 0 + x = -6.557438524 + 8 x = -6.557438524 + 8 Combine like terms: -6.557438524 + 8 = 1.442561476 x = 1.442561476 Simplifying x = 1.442561476Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.557438524, 1.442561476}
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