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Simplifying 0.6(x2) + -21x + 180 = 0 Reorder the terms: 180 + -21x + 0.6x2 = 0 Solving 180 + -21x + 0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. 300 + -35x + x2 = 0 Move the constant term to the right: Add '-300' to each side of the equation. 300 + -35x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -35x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -35x + x2 = 0 + -300 -35x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -35x + x2 = -300 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 = -300 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -300 + 306.25 Combine like terms: -300 + 306.25 = 6.25 306.25 + -35x + x2 = 6.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -17.5) equal to 2.5 and -2.5.Subproblem 1
x + -17.5 = 2.5 Simplifying x + -17.5 = 2.5 Reorder the terms: -17.5 + x = 2.5 Solving -17.5 + x = 2.5 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 = 2.5 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 2.5 + 17.5 x = 2.5 + 17.5 Combine like terms: 2.5 + 17.5 = 20 x = 20 Simplifying x = 20Subproblem 2
x + -17.5 = -2.5 Simplifying x + -17.5 = -2.5 Reorder the terms: -17.5 + x = -2.5 Solving -17.5 + x = -2.5 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 = -2.5 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -2.5 + 17.5 x = -2.5 + 17.5 Combine like terms: -2.5 + 17.5 = 15 x = 15 Simplifying x = 15Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, 15}
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