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Simplifying -0.15 + 2.2x + 1.1x2 = 0 Solving -0.15 + 2.2x + 1.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.1 the coefficient of the squared term: Divide each side by '1.1'. -0.1363636364 + 2x + x2 = 0 Move the constant term to the right: Add '0.1363636364' to each side of the equation. -0.1363636364 + 2x + 0.1363636364 + x2 = 0 + 0.1363636364 Reorder the terms: -0.1363636364 + 0.1363636364 + 2x + x2 = 0 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + 0.1363636364 2x + x2 = 0 + 0.1363636364 Combine like terms: 0 + 0.1363636364 = 0.1363636364 2x + x2 = 0.1363636364 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 = 0.1363636364 + 1 Reorder the terms: 1 + 2x + x2 = 0.1363636364 + 1 Combine like terms: 0.1363636364 + 1 = 1.1363636364 1 + 2x + x2 = 1.1363636364 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.1363636364 Calculate the square root of the right side: 1.066003582 Break this problem into two subproblems by setting (x + 1) equal to 1.066003582 and -1.066003582.Subproblem 1
x + 1 = 1.066003582 Simplifying x + 1 = 1.066003582 Reorder the terms: 1 + x = 1.066003582 Solving 1 + x = 1.066003582 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 = 1.066003582 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.066003582 + -1 x = 1.066003582 + -1 Combine like terms: 1.066003582 + -1 = 0.066003582 x = 0.066003582 Simplifying x = 0.066003582Subproblem 2
x + 1 = -1.066003582 Simplifying x + 1 = -1.066003582 Reorder the terms: 1 + x = -1.066003582 Solving 1 + x = -1.066003582 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 = -1.066003582 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.066003582 + -1 x = -1.066003582 + -1 Combine like terms: -1.066003582 + -1 = -2.066003582 x = -2.066003582 Simplifying x = -2.066003582Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.066003582, -2.066003582}
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