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Simplifying 0.7 = x2 + 2x Reorder the terms: 0.7 = 2x + x2 Solving 0.7 = 2x + x2 Solving for variable 'x'. Reorder the terms: 0.7 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 0.7 + -2x + -1x2 = 0 + x2 + -1x2 0.7 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.7 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.7 + 2x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 2x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + 2x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 2x + x2 = 0 + 0.7 2x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 2x + x2 = 0.7 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.7 + 1 Reorder the terms: 1 + 2x + x2 = 0.7 + 1 Combine like terms: 0.7 + 1 = 1.7 1 + 2x + x2 = 1.7 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.7 Calculate the square root of the right side: 1.303840481 Break this problem into two subproblems by setting (x + 1) equal to 1.303840481 and -1.303840481.Subproblem 1
x + 1 = 1.303840481 Simplifying x + 1 = 1.303840481 Reorder the terms: 1 + x = 1.303840481 Solving 1 + x = 1.303840481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.303840481 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.303840481 + -1 x = 1.303840481 + -1 Combine like terms: 1.303840481 + -1 = 0.303840481 x = 0.303840481 Simplifying x = 0.303840481Subproblem 2
x + 1 = -1.303840481 Simplifying x + 1 = -1.303840481 Reorder the terms: 1 + x = -1.303840481 Solving 1 + x = -1.303840481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.303840481 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.303840481 + -1 x = -1.303840481 + -1 Combine like terms: -1.303840481 + -1 = -2.303840481 x = -2.303840481 Simplifying x = -2.303840481Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.303840481, -2.303840481}
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