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Simplifying 0.2x2 + -16x + 300 = 0 Reorder the terms: 300 + -16x + 0.2x2 = 0 Solving 300 + -16x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 1500 + -80x + x2 = 0 Move the constant term to the right: Add '-1500' to each side of the equation. 1500 + -80x + -1500 + x2 = 0 + -1500 Reorder the terms: 1500 + -1500 + -80x + x2 = 0 + -1500 Combine like terms: 1500 + -1500 = 0 0 + -80x + x2 = 0 + -1500 -80x + x2 = 0 + -1500 Combine like terms: 0 + -1500 = -1500 -80x + x2 = -1500 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = -1500 + 1600 Reorder the terms: 1600 + -80x + x2 = -1500 + 1600 Combine like terms: -1500 + 1600 = 100 1600 + -80x + x2 = 100 Factor a perfect square on the left side: (x + -40)(x + -40) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + -40) equal to 10 and -10.Subproblem 1
x + -40 = 10 Simplifying x + -40 = 10 Reorder the terms: -40 + x = 10 Solving -40 + x = 10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 10 + 40 Combine like terms: -40 + 40 = 0 0 + x = 10 + 40 x = 10 + 40 Combine like terms: 10 + 40 = 50 x = 50 Simplifying x = 50Subproblem 2
x + -40 = -10 Simplifying x + -40 = -10 Reorder the terms: -40 + x = -10 Solving -40 + x = -10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -10 + 40 Combine like terms: -40 + 40 = 0 0 + x = -10 + 40 x = -10 + 40 Combine like terms: -10 + 40 = 30 x = 30 Simplifying x = 30Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, 30}
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