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Simplifying x2 + 8x = 154 Reorder the terms: 8x + x2 = 154 Solving 8x + x2 = 154 Solving for variable 'x'. Reorder the terms: -154 + 8x + x2 = 154 + -154 Combine like terms: 154 + -154 = 0 -154 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '154' to each side of the equation. -154 + 8x + 154 + x2 = 0 + 154 Reorder the terms: -154 + 154 + 8x + x2 = 0 + 154 Combine like terms: -154 + 154 = 0 0 + 8x + x2 = 0 + 154 8x + x2 = 0 + 154 Combine like terms: 0 + 154 = 154 8x + x2 = 154 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 = 154 + 16 Reorder the terms: 16 + 8x + x2 = 154 + 16 Combine like terms: 154 + 16 = 170 16 + 8x + x2 = 170 Factor a perfect square on the left side: (x + 4)(x + 4) = 170 Calculate the square root of the right side: 13.03840481 Break this problem into two subproblems by setting (x + 4) equal to 13.03840481 and -13.03840481.Subproblem 1
x + 4 = 13.03840481 Simplifying x + 4 = 13.03840481 Reorder the terms: 4 + x = 13.03840481 Solving 4 + x = 13.03840481 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 = 13.03840481 + -4 Combine like terms: 4 + -4 = 0 0 + x = 13.03840481 + -4 x = 13.03840481 + -4 Combine like terms: 13.03840481 + -4 = 9.03840481 x = 9.03840481 Simplifying x = 9.03840481Subproblem 2
x + 4 = -13.03840481 Simplifying x + 4 = -13.03840481 Reorder the terms: 4 + x = -13.03840481 Solving 4 + x = -13.03840481 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 = -13.03840481 + -4 Combine like terms: 4 + -4 = 0 0 + x = -13.03840481 + -4 x = -13.03840481 + -4 Combine like terms: -13.03840481 + -4 = -17.03840481 x = -17.03840481 Simplifying x = -17.03840481Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.03840481, -17.03840481}
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