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Simplifying 2x2 + -22x + 28.5 = 0 Reorder the terms: 28.5 + -22x + 2x2 = 0 Solving 28.5 + -22x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14.25 + -11x + x2 = 0 Move the constant term to the right: Add '-14.25' to each side of the equation. 14.25 + -11x + -14.25 + x2 = 0 + -14.25 Reorder the terms: 14.25 + -14.25 + -11x + x2 = 0 + -14.25 Combine like terms: 14.25 + -14.25 = 0.00 0.00 + -11x + x2 = 0 + -14.25 -11x + x2 = 0 + -14.25 Combine like terms: 0 + -14.25 = -14.25 -11x + x2 = -14.25 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 = -14.25 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -14.25 + 30.25 Combine like terms: -14.25 + 30.25 = 16 30.25 + -11x + x2 = 16 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + -5.5) equal to 4 and -4.Subproblem 1
x + -5.5 = 4 Simplifying x + -5.5 = 4 Reorder the terms: -5.5 + x = 4 Solving -5.5 + x = 4 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 = 4 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 4 + 5.5 x = 4 + 5.5 Combine like terms: 4 + 5.5 = 9.5 x = 9.5 Simplifying x = 9.5Subproblem 2
x + -5.5 = -4 Simplifying x + -5.5 = -4 Reorder the terms: -5.5 + x = -4 Solving -5.5 + x = -4 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 = -4 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -4 + 5.5 x = -4 + 5.5 Combine like terms: -4 + 5.5 = 1.5 x = 1.5 Simplifying x = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.5, 1.5}
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