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Simplifying -0.25x2 + 2.75x + 3 = 0 Reorder the terms: 3 + 2.75x + -0.25x2 = 0 Solving 3 + 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'. -12 + -11x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -11x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -11x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -11x + x2 = 0 + 12 -11x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -11x + x2 = 12 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 = 12 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 12 + 30.25 Combine like terms: 12 + 30.25 = 42.25 30.25 + -11x + x2 = 42.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 42.25 Calculate the square root of the right side: 6.5 Break this problem into two subproblems by setting (x + -5.5) equal to 6.5 and -6.5.Subproblem 1
x + -5.5 = 6.5 Simplifying x + -5.5 = 6.5 Reorder the terms: -5.5 + x = 6.5 Solving -5.5 + x = 6.5 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 = 6.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.5 + 5.5 x = 6.5 + 5.5 Combine like terms: 6.5 + 5.5 = 12 x = 12 Simplifying x = 12Subproblem 2
x + -5.5 = -6.5 Simplifying x + -5.5 = -6.5 Reorder the terms: -5.5 + x = -6.5 Solving -5.5 + x = -6.5 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 = -6.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.5 + 5.5 x = -6.5 + 5.5 Combine like terms: -6.5 + 5.5 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {12, -1}
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