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Simplifying (2.5x + -5)(x + -9) = 0 Reorder the terms: (-5 + 2.5x)(x + -9) = 0 Reorder the terms: (-5 + 2.5x)(-9 + x) = 0 Multiply (-5 + 2.5x) * (-9 + x) (-5(-9 + x) + 2.5x * (-9 + x)) = 0 ((-9 * -5 + x * -5) + 2.5x * (-9 + x)) = 0 ((45 + -5x) + 2.5x * (-9 + x)) = 0 (45 + -5x + (-9 * 2.5x + x * 2.5x)) = 0 (45 + -5x + (-22.5x + 2.5x2)) = 0 Combine like terms: -5x + -22.5x = -27.5x (45 + -27.5x + 2.5x2) = 0 Solving 45 + -27.5x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 18 + -11x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -11x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -11x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -11x + x2 = 0 + -18 -11x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -11x + x2 = -18 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 = -18 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -18 + 30.25 Combine like terms: -18 + 30.25 = 12.25 30.25 + -11x + x2 = 12.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting (x + -5.5) equal to 3.5 and -3.5.Subproblem 1
x + -5.5 = 3.5 Simplifying x + -5.5 = 3.5 Reorder the terms: -5.5 + x = 3.5 Solving -5.5 + x = 3.5 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 = 3.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 3.5 + 5.5 x = 3.5 + 5.5 Combine like terms: 3.5 + 5.5 = 9 x = 9 Simplifying x = 9Subproblem 2
x + -5.5 = -3.5 Simplifying x + -5.5 = -3.5 Reorder the terms: -5.5 + x = -3.5 Solving -5.5 + x = -3.5 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 = -3.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -3.5 + 5.5 x = -3.5 + 5.5 Combine like terms: -3.5 + 5.5 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {9, 2}
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