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Simplifying 0 = -0.5x2 + 40x + -300 Reorder the terms: 0 = -300 + 40x + -0.5x2 Solving 0 = -300 + 40x + -0.5x2 Solving for variable 'x'. Combine like terms: 0 + 300 = 300 300 + -40x + 0.5x2 = -300 + 40x + -0.5x2 + 300 + -40x + 0.5x2 Reorder the terms: 300 + -40x + 0.5x2 = -300 + 300 + 40x + -40x + -0.5x2 + 0.5x2 Combine like terms: -300 + 300 = 0 300 + -40x + 0.5x2 = 0 + 40x + -40x + -0.5x2 + 0.5x2 300 + -40x + 0.5x2 = 40x + -40x + -0.5x2 + 0.5x2 Combine like terms: 40x + -40x = 0 300 + -40x + 0.5x2 = 0 + -0.5x2 + 0.5x2 300 + -40x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 300 + -40x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 600 + -80x + x2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + -80x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -80x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -80x + x2 = 0 + -600 -80x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -80x + x2 = -600 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 = -600 + 1600 Reorder the terms: 1600 + -80x + x2 = -600 + 1600 Combine like terms: -600 + 1600 = 1000 1600 + -80x + x2 = 1000 Factor a perfect square on the left side: (x + -40)(x + -40) = 1000 Calculate the square root of the right side: 31.622776602 Break this problem into two subproblems by setting (x + -40) equal to 31.622776602 and -31.622776602.Subproblem 1
x + -40 = 31.622776602 Simplifying x + -40 = 31.622776602 Reorder the terms: -40 + x = 31.622776602 Solving -40 + x = 31.622776602 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 = 31.622776602 + 40 Combine like terms: -40 + 40 = 0 0 + x = 31.622776602 + 40 x = 31.622776602 + 40 Combine like terms: 31.622776602 + 40 = 71.622776602 x = 71.622776602 Simplifying x = 71.622776602Subproblem 2
x + -40 = -31.622776602 Simplifying x + -40 = -31.622776602 Reorder the terms: -40 + x = -31.622776602 Solving -40 + x = -31.622776602 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 = -31.622776602 + 40 Combine like terms: -40 + 40 = 0 0 + x = -31.622776602 + 40 x = -31.622776602 + 40 Combine like terms: -31.622776602 + 40 = 8.377223398 x = 8.377223398 Simplifying x = 8.377223398Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.622776602, 8.377223398}
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