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Simplifying -0.05x2 + 1.75x + 22.5 = 0 Reorder the terms: 22.5 + 1.75x + -0.05x2 = 0 Solving 22.5 + 1.75x + -0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -450 + -35x + x2 = 0 Move the constant term to the right: Add '450' to each side of the equation. -450 + -35x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + -35x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + -35x + x2 = 0 + 450 -35x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 -35x + x2 = 450 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = 450 + 306.25 Reorder the terms: 306.25 + -35x + x2 = 450 + 306.25 Combine like terms: 450 + 306.25 = 756.25 306.25 + -35x + x2 = 756.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 756.25 Calculate the square root of the right side: 27.5 Break this problem into two subproblems by setting (x + -17.5) equal to 27.5 and -27.5.Subproblem 1
x + -17.5 = 27.5 Simplifying x + -17.5 = 27.5 Reorder the terms: -17.5 + x = 27.5 Solving -17.5 + x = 27.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 27.5 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 27.5 + 17.5 x = 27.5 + 17.5 Combine like terms: 27.5 + 17.5 = 45 x = 45 Simplifying x = 45Subproblem 2
x + -17.5 = -27.5 Simplifying x + -17.5 = -27.5 Reorder the terms: -17.5 + x = -27.5 Solving -17.5 + x = -27.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -27.5 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -27.5 + 17.5 x = -27.5 + 17.5 Combine like terms: -27.5 + 17.5 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {45, -10}
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