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Simplifying -0.02x2 + 162x + -16000 = 0 Reorder the terms: -16000 + 162x + -0.02x2 = 0 Solving -16000 + 162x + -0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 800000 + -8100x + x2 = 0 Move the constant term to the right: Add '-800000' to each side of the equation. 800000 + -8100x + -800000 + x2 = 0 + -800000 Reorder the terms: 800000 + -800000 + -8100x + x2 = 0 + -800000 Combine like terms: 800000 + -800000 = 0 0 + -8100x + x2 = 0 + -800000 -8100x + x2 = 0 + -800000 Combine like terms: 0 + -800000 = -800000 -8100x + x2 = -800000 The x term is -8100x. Take half its coefficient (-4050). Square it (16402500) and add it to both sides. Add '16402500' to each side of the equation. -8100x + 16402500 + x2 = -800000 + 16402500 Reorder the terms: 16402500 + -8100x + x2 = -800000 + 16402500 Combine like terms: -800000 + 16402500 = 15602500 16402500 + -8100x + x2 = 15602500 Factor a perfect square on the left side: (x + -4050)(x + -4050) = 15602500 Calculate the square root of the right side: 3950 Break this problem into two subproblems by setting (x + -4050) equal to 3950 and -3950.Subproblem 1
x + -4050 = 3950 Simplifying x + -4050 = 3950 Reorder the terms: -4050 + x = 3950 Solving -4050 + x = 3950 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4050' to each side of the equation. -4050 + 4050 + x = 3950 + 4050 Combine like terms: -4050 + 4050 = 0 0 + x = 3950 + 4050 x = 3950 + 4050 Combine like terms: 3950 + 4050 = 8000 x = 8000 Simplifying x = 8000Subproblem 2
x + -4050 = -3950 Simplifying x + -4050 = -3950 Reorder the terms: -4050 + x = -3950 Solving -4050 + x = -3950 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4050' to each side of the equation. -4050 + 4050 + x = -3950 + 4050 Combine like terms: -4050 + 4050 = 0 0 + x = -3950 + 4050 x = -3950 + 4050 Combine like terms: -3950 + 4050 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {8000, 100}
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