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Simplifying 0 = 100 + -0.3x + -0.0006x2 Solving 0 = 100 + -0.3x + -0.0006x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + 0.3x + 0.0006x2 = 100 + -0.3x + -0.0006x2 + -100 + 0.3x + 0.0006x2 Reorder the terms: -100 + 0.3x + 0.0006x2 = 100 + -100 + -0.3x + 0.3x + -0.0006x2 + 0.0006x2 Combine like terms: 100 + -100 = 0 -100 + 0.3x + 0.0006x2 = 0 + -0.3x + 0.3x + -0.0006x2 + 0.0006x2 -100 + 0.3x + 0.0006x2 = -0.3x + 0.3x + -0.0006x2 + 0.0006x2 Combine like terms: -0.3x + 0.3x = 0.0 -100 + 0.3x + 0.0006x2 = 0.0 + -0.0006x2 + 0.0006x2 -100 + 0.3x + 0.0006x2 = -0.0006x2 + 0.0006x2 Combine like terms: -0.0006x2 + 0.0006x2 = 0.0000 -100 + 0.3x + 0.0006x2 = 0.0000 Begin completing the square. Divide all terms by 0.0006 the coefficient of the squared term: Divide each side by '0.0006'. -166666.6667 + 500x + x2 = 0 Move the constant term to the right: Add '166666.6667' to each side of the equation. -166666.6667 + 500x + 166666.6667 + x2 = 0 + 166666.6667 Reorder the terms: -166666.6667 + 166666.6667 + 500x + x2 = 0 + 166666.6667 Combine like terms: -166666.6667 + 166666.6667 = 0.0000 0.0000 + 500x + x2 = 0 + 166666.6667 500x + x2 = 0 + 166666.6667 Combine like terms: 0 + 166666.6667 = 166666.6667 500x + x2 = 166666.6667 The x term is 500x. Take half its coefficient (250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. 500x + 62500 + x2 = 166666.6667 + 62500 Reorder the terms: 62500 + 500x + x2 = 166666.6667 + 62500 Combine like terms: 166666.6667 + 62500 = 229166.6667 62500 + 500x + x2 = 229166.6667 Factor a perfect square on the left side: (x + 250)(x + 250) = 229166.6667 Calculate the square root of the right side: 478.713553913 Break this problem into two subproblems by setting (x + 250) equal to 478.713553913 and -478.713553913.Subproblem 1
x + 250 = 478.713553913 Simplifying x + 250 = 478.713553913 Reorder the terms: 250 + x = 478.713553913 Solving 250 + x = 478.713553913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 478.713553913 + -250 Combine like terms: 250 + -250 = 0 0 + x = 478.713553913 + -250 x = 478.713553913 + -250 Combine like terms: 478.713553913 + -250 = 228.713553913 x = 228.713553913 Simplifying x = 228.713553913Subproblem 2
x + 250 = -478.713553913 Simplifying x + 250 = -478.713553913 Reorder the terms: 250 + x = -478.713553913 Solving 250 + x = -478.713553913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = -478.713553913 + -250 Combine like terms: 250 + -250 = 0 0 + x = -478.713553913 + -250 x = -478.713553913 + -250 Combine like terms: -478.713553913 + -250 = -728.713553913 x = -728.713553913 Simplifying x = -728.713553913Solution
The solution to the problem is based on the solutions from the subproblems. x = {228.713553913, -728.713553913}
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