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Simplifying 0.25x2 + 2.75x + 6 = 0 Reorder the terms: 6 + 2.75x + 0.25x2 = 0 Solving 6 + 2.75x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 24 + 11x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + 11x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 11x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 11x + x2 = 0 + -24 11x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 11x + x2 = -24 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -24 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -24 + 30.25 Combine like terms: -24 + 30.25 = 6.25 30.25 + 11x + x2 = 6.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + 5.5) equal to 2.5 and -2.5.Subproblem 1
x + 5.5 = 2.5 Simplifying x + 5.5 = 2.5 Reorder the terms: 5.5 + x = 2.5 Solving 5.5 + x = 2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 2.5 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 2.5 + -5.5 x = 2.5 + -5.5 Combine like terms: 2.5 + -5.5 = -3 x = -3 Simplifying x = -3Subproblem 2
x + 5.5 = -2.5 Simplifying x + 5.5 = -2.5 Reorder the terms: 5.5 + x = -2.5 Solving 5.5 + x = -2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -2.5 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -2.5 + -5.5 x = -2.5 + -5.5 Combine like terms: -2.5 + -5.5 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3, -8}
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