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Simplifying 0.2x2 + -1.1x + 0.5 = 0 Reorder the terms: 0.5 + -1.1x + 0.2x2 = 0 Solving 0.5 + -1.1x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 2.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -5.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -5.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -5.5x + x2 = 0 + -2.5 -5.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -5.5x + x2 = -2.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -2.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -2.5 + 7.5625 Combine like terms: -2.5 + 7.5625 = 5.0625 7.5625 + -5.5x + x2 = 5.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + -2.75) equal to 2.25 and -2.25.Subproblem 1
x + -2.75 = 2.25 Simplifying x + -2.75 = 2.25 Reorder the terms: -2.75 + x = 2.25 Solving -2.75 + x = 2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.25 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.25 + 2.75 x = 2.25 + 2.75 Combine like terms: 2.25 + 2.75 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -2.75 = -2.25 Simplifying x + -2.75 = -2.25 Reorder the terms: -2.75 + x = -2.25 Solving -2.75 + x = -2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.25 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.25 + 2.75 x = -2.25 + 2.75 Combine like terms: -2.25 + 2.75 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, 0.5}
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