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Simplifying 0 = -1(0.05) * x2 + x + 40 Multiply -1 * 0.05 0 = -0.05x2 + x + 40 Reorder the terms: 0 = 40 + x + -0.05x2 Solving 0 = 40 + x + -0.05x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + -1x + 0.05x2 = 40 + x + -0.05x2 + -40 + -1x + 0.05x2 Reorder the terms: -40 + -1x + 0.05x2 = 40 + -40 + x + -1x + -0.05x2 + 0.05x2 Combine like terms: 40 + -40 = 0 -40 + -1x + 0.05x2 = 0 + x + -1x + -0.05x2 + 0.05x2 -40 + -1x + 0.05x2 = x + -1x + -0.05x2 + 0.05x2 Combine like terms: x + -1x = 0 -40 + -1x + 0.05x2 = 0 + -0.05x2 + 0.05x2 -40 + -1x + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 -40 + -1x + 0.05x2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -800 + -20x + x2 = 0 Move the constant term to the right: Add '800' to each side of the equation. -800 + -20x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + -20x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + -20x + x2 = 0 + 800 -20x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 -20x + x2 = 800 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 800 + 100 Reorder the terms: 100 + -20x + x2 = 800 + 100 Combine like terms: 800 + 100 = 900 100 + -20x + x2 = 900 Factor a perfect square on the left side: (x + -10)(x + -10) = 900 Calculate the square root of the right side: 30 Break this problem into two subproblems by setting (x + -10) equal to 30 and -30.Subproblem 1
x + -10 = 30 Simplifying x + -10 = 30 Reorder the terms: -10 + x = 30 Solving -10 + x = 30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 30 + 10 Combine like terms: -10 + 10 = 0 0 + x = 30 + 10 x = 30 + 10 Combine like terms: 30 + 10 = 40 x = 40 Simplifying x = 40Subproblem 2
x + -10 = -30 Simplifying x + -10 = -30 Reorder the terms: -10 + x = -30 Solving -10 + x = -30 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -30 + 10 Combine like terms: -10 + 10 = 0 0 + x = -30 + 10 x = -30 + 10 Combine like terms: -30 + 10 = -20 x = -20 Simplifying x = -20Solution
The solution to the problem is based on the solutions from the subproblems. x = {40, -20}
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