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Simplifying -0.004x2 + 3.2x + -150 = 0 Reorder the terms: -150 + 3.2x + -0.004x2 = 0 Solving -150 + 3.2x + -0.004x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.004 the coefficient of the squared term: Divide each side by '-0.004'. 37500 + -800x + x2 = 0 Move the constant term to the right: Add '-37500' to each side of the equation. 37500 + -800x + -37500 + x2 = 0 + -37500 Reorder the terms: 37500 + -37500 + -800x + x2 = 0 + -37500 Combine like terms: 37500 + -37500 = 0 0 + -800x + x2 = 0 + -37500 -800x + x2 = 0 + -37500 Combine like terms: 0 + -37500 = -37500 -800x + x2 = -37500 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 = -37500 + 160000 Reorder the terms: 160000 + -800x + x2 = -37500 + 160000 Combine like terms: -37500 + 160000 = 122500 160000 + -800x + x2 = 122500 Factor a perfect square on the left side: (x + -400)(x + -400) = 122500 Calculate the square root of the right side: 350 Break this problem into two subproblems by setting (x + -400) equal to 350 and -350.Subproblem 1
x + -400 = 350 Simplifying x + -400 = 350 Reorder the terms: -400 + x = 350 Solving -400 + x = 350 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 = 350 + 400 Combine like terms: -400 + 400 = 0 0 + x = 350 + 400 x = 350 + 400 Combine like terms: 350 + 400 = 750 x = 750 Simplifying x = 750Subproblem 2
x + -400 = -350 Simplifying x + -400 = -350 Reorder the terms: -400 + x = -350 Solving -400 + x = -350 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 = -350 + 400 Combine like terms: -400 + 400 = 0 0 + x = -350 + 400 x = -350 + 400 Combine like terms: -350 + 400 = 50 x = 50 Simplifying x = 50Solution
The solution to the problem is based on the solutions from the subproblems. x = {750, 50}
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