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Simplifying 0 = x2 + -16x + 8 Reorder the terms: 0 = 8 + -16x + x2 Solving 0 = 8 + -16x + x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + 16x + -1x2 = 8 + -16x + x2 + -8 + 16x + -1x2 Reorder the terms: -8 + 16x + -1x2 = 8 + -8 + -16x + 16x + x2 + -1x2 Combine like terms: 8 + -8 = 0 -8 + 16x + -1x2 = 0 + -16x + 16x + x2 + -1x2 -8 + 16x + -1x2 = -16x + 16x + x2 + -1x2 Combine like terms: -16x + 16x = 0 -8 + 16x + -1x2 = 0 + x2 + -1x2 -8 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -16x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -16x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -16x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -16x + x2 = 0 + -8 -16x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -16x + x2 = -8 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 = -8 + 64 Reorder the terms: 64 + -16x + x2 = -8 + 64 Combine like terms: -8 + 64 = 56 64 + -16x + x2 = 56 Factor a perfect square on the left side: (x + -8)(x + -8) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + -8) equal to 7.483314774 and -7.483314774.Subproblem 1
x + -8 = 7.483314774 Simplifying x + -8 = 7.483314774 Reorder the terms: -8 + x = 7.483314774 Solving -8 + x = 7.483314774 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 = 7.483314774 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.483314774 + 8 x = 7.483314774 + 8 Combine like terms: 7.483314774 + 8 = 15.483314774 x = 15.483314774 Simplifying x = 15.483314774Subproblem 2
x + -8 = -7.483314774 Simplifying x + -8 = -7.483314774 Reorder the terms: -8 + x = -7.483314774 Solving -8 + x = -7.483314774 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 = -7.483314774 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.483314774 + 8 x = -7.483314774 + 8 Combine like terms: -7.483314774 + 8 = 0.516685226 x = 0.516685226 Simplifying x = 0.516685226Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.483314774, 0.516685226}
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