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Simplifying 15000 + -160x + 0.1x2 = 0 Solving 15000 + -160x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 150000 + -1600x + x2 = 0 Move the constant term to the right: Add '-150000' to each side of the equation. 150000 + -1600x + -150000 + x2 = 0 + -150000 Reorder the terms: 150000 + -150000 + -1600x + x2 = 0 + -150000 Combine like terms: 150000 + -150000 = 0 0 + -1600x + x2 = 0 + -150000 -1600x + x2 = 0 + -150000 Combine like terms: 0 + -150000 = -150000 -1600x + x2 = -150000 The x term is -1600x. Take half its coefficient (-800). Square it (640000) and add it to both sides. Add '640000' to each side of the equation. -1600x + 640000 + x2 = -150000 + 640000 Reorder the terms: 640000 + -1600x + x2 = -150000 + 640000 Combine like terms: -150000 + 640000 = 490000 640000 + -1600x + x2 = 490000 Factor a perfect square on the left side: (x + -800)(x + -800) = 490000 Calculate the square root of the right side: 700 Break this problem into two subproblems by setting (x + -800) equal to 700 and -700.Subproblem 1
x + -800 = 700 Simplifying x + -800 = 700 Reorder the terms: -800 + x = 700 Solving -800 + x = 700 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '800' to each side of the equation. -800 + 800 + x = 700 + 800 Combine like terms: -800 + 800 = 0 0 + x = 700 + 800 x = 700 + 800 Combine like terms: 700 + 800 = 1500 x = 1500 Simplifying x = 1500Subproblem 2
x + -800 = -700 Simplifying x + -800 = -700 Reorder the terms: -800 + x = -700 Solving -800 + x = -700 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '800' to each side of the equation. -800 + 800 + x = -700 + 800 Combine like terms: -800 + 800 = 0 0 + x = -700 + 800 x = -700 + 800 Combine like terms: -700 + 800 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {1500, 100}
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