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Simplifying -0.004x2 + 3.2x + -150 = 400 Reorder the terms: -150 + 3.2x + -0.004x2 = 400 Solving -150 + 3.2x + -0.004x2 = 400 Solving for variable 'x'. Reorder the terms: -150 + -400 + 3.2x + -0.004x2 = 400 + -400 Combine like terms: -150 + -400 = -550 -550 + 3.2x + -0.004x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -550 + 3.2x + -0.004x2 = 0 Begin completing the square. Divide all terms by -0.004 the coefficient of the squared term: Divide each side by '-0.004'. 137500 + -800x + x2 = 0 Move the constant term to the right: Add '-137500' to each side of the equation. 137500 + -800x + -137500 + x2 = 0 + -137500 Reorder the terms: 137500 + -137500 + -800x + x2 = 0 + -137500 Combine like terms: 137500 + -137500 = 0 0 + -800x + x2 = 0 + -137500 -800x + x2 = 0 + -137500 Combine like terms: 0 + -137500 = -137500 -800x + x2 = -137500 The x term is -800x. Take half its coefficient (-400). Square it (160000) and add it to both sides. Add '160000' to each side of the equation. -800x + 160000 + x2 = -137500 + 160000 Reorder the terms: 160000 + -800x + x2 = -137500 + 160000 Combine like terms: -137500 + 160000 = 22500 160000 + -800x + x2 = 22500 Factor a perfect square on the left side: (x + -400)(x + -400) = 22500 Calculate the square root of the right side: 150 Break this problem into two subproblems by setting (x + -400) equal to 150 and -150.Subproblem 1
x + -400 = 150 Simplifying x + -400 = 150 Reorder the terms: -400 + x = 150 Solving -400 + x = 150 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = 150 + 400 Combine like terms: -400 + 400 = 0 0 + x = 150 + 400 x = 150 + 400 Combine like terms: 150 + 400 = 550 x = 550 Simplifying x = 550Subproblem 2
x + -400 = -150 Simplifying x + -400 = -150 Reorder the terms: -400 + x = -150 Solving -400 + x = -150 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = -150 + 400 Combine like terms: -400 + 400 = 0 0 + x = -150 + 400 x = -150 + 400 Combine like terms: -150 + 400 = 250 x = 250 Simplifying x = 250Solution
The solution to the problem is based on the solutions from the subproblems. x = {550, 250}
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