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Simplifying 164(x) = x2 + -8x + 16 Reorder the terms: 164x = 16 + -8x + x2 Solving 164x = 16 + -8x + x2 Solving for variable 'x'. Reorder the terms: -16 + 164x + 8x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2 Combine like terms: 164x + 8x = 172x -16 + 172x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2 Reorder the terms: -16 + 172x + -1x2 = 16 + -16 + -8x + 8x + x2 + -1x2 Combine like terms: 16 + -16 = 0 -16 + 172x + -1x2 = 0 + -8x + 8x + x2 + -1x2 -16 + 172x + -1x2 = -8x + 8x + x2 + -1x2 Combine like terms: -8x + 8x = 0 -16 + 172x + -1x2 = 0 + x2 + -1x2 -16 + 172x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -16 + 172x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 16 + -172x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -172x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -172x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -172x + x2 = 0 + -16 -172x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -172x + x2 = -16 The x term is -172x. Take half its coefficient (-86). Square it (7396) and add it to both sides. Add '7396' to each side of the equation. -172x + 7396 + x2 = -16 + 7396 Reorder the terms: 7396 + -172x + x2 = -16 + 7396 Combine like terms: -16 + 7396 = 7380 7396 + -172x + x2 = 7380 Factor a perfect square on the left side: (x + -86)(x + -86) = 7380 Calculate the square root of the right side: 85.90692638 Break this problem into two subproblems by setting (x + -86) equal to 85.90692638 and -85.90692638.Subproblem 1
x + -86 = 85.90692638 Simplifying x + -86 = 85.90692638 Reorder the terms: -86 + x = 85.90692638 Solving -86 + x = 85.90692638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '86' to each side of the equation. -86 + 86 + x = 85.90692638 + 86 Combine like terms: -86 + 86 = 0 0 + x = 85.90692638 + 86 x = 85.90692638 + 86 Combine like terms: 85.90692638 + 86 = 171.90692638 x = 171.90692638 Simplifying x = 171.90692638Subproblem 2
x + -86 = -85.90692638 Simplifying x + -86 = -85.90692638 Reorder the terms: -86 + x = -85.90692638 Solving -86 + x = -85.90692638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '86' to each side of the equation. -86 + 86 + x = -85.90692638 + 86 Combine like terms: -86 + 86 = 0 0 + x = -85.90692638 + 86 x = -85.90692638 + 86 Combine like terms: -85.90692638 + 86 = 0.09307362 x = 0.09307362 Simplifying x = 0.09307362Solution
The solution to the problem is based on the solutions from the subproblems. x = {171.90692638, 0.09307362}
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