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Simplifying 2x2 + 2x + 1 = 3.6055 Reorder the terms: 1 + 2x + 2x2 = 3.6055 Solving 1 + 2x + 2x2 = 3.6055 Solving for variable 'x'. Reorder the terms: 1 + -3.6055 + 2x + 2x2 = 3.6055 + -3.6055 Combine like terms: 1 + -3.6055 = -2.6055 -2.6055 + 2x + 2x2 = 3.6055 + -3.6055 Combine like terms: 3.6055 + -3.6055 = 0.0000 -2.6055 + 2x + 2x2 = 0.0000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.30275 + x + x2 = 0.0000 Move the constant term to the right: Add '1.30275' to each side of the equation. -1.30275 + x + 1.30275 + x2 = 0.0000 + 1.30275 Reorder the terms: -1.30275 + 1.30275 + x + x2 = 0.0000 + 1.30275 Combine like terms: -1.30275 + 1.30275 = 0.00000 0.00000 + x + x2 = 0.0000 + 1.30275 x + x2 = 0.0000 + 1.30275 Combine like terms: 0.0000 + 1.30275 = 1.30275 x + x2 = 1.30275 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.30275 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.30275 + 0.25 Combine like terms: 1.30275 + 0.25 = 1.55275 1.25 + x2 = 1.55275 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.55275 Calculate the square root of the right side: 1.246093897 Break this problem into two subproblems by setting (x + 0.5) equal to 1.246093897 and -1.246093897.Subproblem 1
x + 0.5 = 1.246093897 Simplifying x + 0.5 = 1.246093897 Reorder the terms: 0.5 + x = 1.246093897 Solving 0.5 + x = 1.246093897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.246093897 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.246093897 + -0.5 x = 1.246093897 + -0.5 Combine like terms: 1.246093897 + -0.5 = 0.746093897 x = 0.746093897 Simplifying x = 0.746093897Subproblem 2
x + 0.5 = -1.246093897 Simplifying x + 0.5 = -1.246093897 Reorder the terms: 0.5 + x = -1.246093897 Solving 0.5 + x = -1.246093897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.246093897 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.246093897 + -0.5 x = -1.246093897 + -0.5 Combine like terms: -1.246093897 + -0.5 = -1.746093897 x = -1.746093897 Simplifying x = -1.746093897Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.746093897, -1.746093897}
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