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Simplifying x2 + -32x + 86 = 0 Reorder the terms: 86 + -32x + x2 = 0 Solving 86 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-86' to each side of the equation. 86 + -32x + -86 + x2 = 0 + -86 Reorder the terms: 86 + -86 + -32x + x2 = 0 + -86 Combine like terms: 86 + -86 = 0 0 + -32x + x2 = 0 + -86 -32x + x2 = 0 + -86 Combine like terms: 0 + -86 = -86 -32x + x2 = -86 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -86 + 256 Reorder the terms: 256 + -32x + x2 = -86 + 256 Combine like terms: -86 + 256 = 170 256 + -32x + x2 = 170 Factor a perfect square on the left side: (x + -16)(x + -16) = 170 Calculate the square root of the right side: 13.03840481 Break this problem into two subproblems by setting (x + -16) equal to 13.03840481 and -13.03840481.Subproblem 1
x + -16 = 13.03840481 Simplifying x + -16 = 13.03840481 Reorder the terms: -16 + x = 13.03840481 Solving -16 + x = 13.03840481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 13.03840481 + 16 Combine like terms: -16 + 16 = 0 0 + x = 13.03840481 + 16 x = 13.03840481 + 16 Combine like terms: 13.03840481 + 16 = 29.03840481 x = 29.03840481 Simplifying x = 29.03840481Subproblem 2
x + -16 = -13.03840481 Simplifying x + -16 = -13.03840481 Reorder the terms: -16 + x = -13.03840481 Solving -16 + x = -13.03840481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -13.03840481 + 16 Combine like terms: -16 + 16 = 0 0 + x = -13.03840481 + 16 x = -13.03840481 + 16 Combine like terms: -13.03840481 + 16 = 2.96159519 x = 2.96159519 Simplifying x = 2.96159519Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.03840481, 2.96159519}
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