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Simplifying x2 + -16x + -34 = 9 Reorder the terms: -34 + -16x + x2 = 9 Solving -34 + -16x + x2 = 9 Solving for variable 'x'. Reorder the terms: -34 + -9 + -16x + x2 = 9 + -9 Combine like terms: -34 + -9 = -43 -43 + -16x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -43 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -16x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + -16x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -16x + x2 = 0 + 43 -16x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 -16x + x2 = 43 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 = 43 + 64 Reorder the terms: 64 + -16x + x2 = 43 + 64 Combine like terms: 43 + 64 = 107 64 + -16x + x2 = 107 Factor a perfect square on the left side: (x + -8)(x + -8) = 107 Calculate the square root of the right side: 10.344080433 Break this problem into two subproblems by setting (x + -8) equal to 10.344080433 and -10.344080433.Subproblem 1
x + -8 = 10.344080433 Simplifying x + -8 = 10.344080433 Reorder the terms: -8 + x = 10.344080433 Solving -8 + x = 10.344080433 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 = 10.344080433 + 8 Combine like terms: -8 + 8 = 0 0 + x = 10.344080433 + 8 x = 10.344080433 + 8 Combine like terms: 10.344080433 + 8 = 18.344080433 x = 18.344080433 Simplifying x = 18.344080433Subproblem 2
x + -8 = -10.344080433 Simplifying x + -8 = -10.344080433 Reorder the terms: -8 + x = -10.344080433 Solving -8 + x = -10.344080433 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 = -10.344080433 + 8 Combine like terms: -8 + 8 = 0 0 + x = -10.344080433 + 8 x = -10.344080433 + 8 Combine like terms: -10.344080433 + 8 = -2.344080433 x = -2.344080433 Simplifying x = -2.344080433Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.344080433, -2.344080433}
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