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Simplifying -0.25x2 + 40x + -1000 = 0 Reorder the terms: -1000 + 40x + -0.25x2 = 0 Solving -1000 + 40x + -0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. 4000 + -160x + x2 = 0 Move the constant term to the right: Add '-4000' to each side of the equation. 4000 + -160x + -4000 + x2 = 0 + -4000 Reorder the terms: 4000 + -4000 + -160x + x2 = 0 + -4000 Combine like terms: 4000 + -4000 = 0 0 + -160x + x2 = 0 + -4000 -160x + x2 = 0 + -4000 Combine like terms: 0 + -4000 = -4000 -160x + x2 = -4000 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = -4000 + 6400 Reorder the terms: 6400 + -160x + x2 = -4000 + 6400 Combine like terms: -4000 + 6400 = 2400 6400 + -160x + x2 = 2400 Factor a perfect square on the left side: (x + -80)(x + -80) = 2400 Calculate the square root of the right side: 48.989794856 Break this problem into two subproblems by setting (x + -80) equal to 48.989794856 and -48.989794856.Subproblem 1
x + -80 = 48.989794856 Simplifying x + -80 = 48.989794856 Reorder the terms: -80 + x = 48.989794856 Solving -80 + x = 48.989794856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 48.989794856 + 80 Combine like terms: -80 + 80 = 0 0 + x = 48.989794856 + 80 x = 48.989794856 + 80 Combine like terms: 48.989794856 + 80 = 128.989794856 x = 128.989794856 Simplifying x = 128.989794856Subproblem 2
x + -80 = -48.989794856 Simplifying x + -80 = -48.989794856 Reorder the terms: -80 + x = -48.989794856 Solving -80 + x = -48.989794856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -48.989794856 + 80 Combine like terms: -80 + 80 = 0 0 + x = -48.989794856 + 80 x = -48.989794856 + 80 Combine like terms: -48.989794856 + 80 = 31.010205144 x = 31.010205144 Simplifying x = 31.010205144Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.989794856, 31.010205144}
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