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Simplifying x2 + 8x + 16 = 1.7 Reorder the terms: 16 + 8x + x2 = 1.7 Solving 16 + 8x + x2 = 1.7 Solving for variable 'x'. Reorder the terms: 16 + -1.7 + 8x + x2 = 1.7 + -1.7 Combine like terms: 16 + -1.7 = 14.3 14.3 + 8x + x2 = 1.7 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 14.3 + 8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-14.3' to each side of the equation. 14.3 + 8x + -14.3 + x2 = 0.0 + -14.3 Reorder the terms: 14.3 + -14.3 + 8x + x2 = 0.0 + -14.3 Combine like terms: 14.3 + -14.3 = 0.0 0.0 + 8x + x2 = 0.0 + -14.3 8x + x2 = 0.0 + -14.3 Combine like terms: 0.0 + -14.3 = -14.3 8x + x2 = -14.3 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -14.3 + 16 Reorder the terms: 16 + 8x + x2 = -14.3 + 16 Combine like terms: -14.3 + 16 = 1.7 16 + 8x + x2 = 1.7 Factor a perfect square on the left side: (x + 4)(x + 4) = 1.7 Calculate the square root of the right side: 1.303840481 Break this problem into two subproblems by setting (x + 4) equal to 1.303840481 and -1.303840481.Subproblem 1
x + 4 = 1.303840481 Simplifying x + 4 = 1.303840481 Reorder the terms: 4 + x = 1.303840481 Solving 4 + x = 1.303840481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 1.303840481 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.303840481 + -4 x = 1.303840481 + -4 Combine like terms: 1.303840481 + -4 = -2.696159519 x = -2.696159519 Simplifying x = -2.696159519Subproblem 2
x + 4 = -1.303840481 Simplifying x + 4 = -1.303840481 Reorder the terms: 4 + x = -1.303840481 Solving 4 + x = -1.303840481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -1.303840481 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.303840481 + -4 x = -1.303840481 + -4 Combine like terms: -1.303840481 + -4 = -5.303840481 x = -5.303840481 Simplifying x = -5.303840481Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.696159519, -5.303840481}
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