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Simplifying -0.004x2 + 3.2x + -200 = 0 Reorder the terms: -200 + 3.2x + -0.004x2 = 0 Solving -200 + 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'. 50000 + -800x + x2 = 0 Move the constant term to the right: Add '-50000' to each side of the equation. 50000 + -800x + -50000 + x2 = 0 + -50000 Reorder the terms: 50000 + -50000 + -800x + x2 = 0 + -50000 Combine like terms: 50000 + -50000 = 0 0 + -800x + x2 = 0 + -50000 -800x + x2 = 0 + -50000 Combine like terms: 0 + -50000 = -50000 -800x + x2 = -50000 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 = -50000 + 160000 Reorder the terms: 160000 + -800x + x2 = -50000 + 160000 Combine like terms: -50000 + 160000 = 110000 160000 + -800x + x2 = 110000 Factor a perfect square on the left side: (x + -400)(x + -400) = 110000 Calculate the square root of the right side: 331.662479036 Break this problem into two subproblems by setting (x + -400) equal to 331.662479036 and -331.662479036.Subproblem 1
x + -400 = 331.662479036 Simplifying x + -400 = 331.662479036 Reorder the terms: -400 + x = 331.662479036 Solving -400 + x = 331.662479036 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 = 331.662479036 + 400 Combine like terms: -400 + 400 = 0 0 + x = 331.662479036 + 400 x = 331.662479036 + 400 Combine like terms: 331.662479036 + 400 = 731.662479036 x = 731.662479036 Simplifying x = 731.662479036Subproblem 2
x + -400 = -331.662479036 Simplifying x + -400 = -331.662479036 Reorder the terms: -400 + x = -331.662479036 Solving -400 + x = -331.662479036 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 = -331.662479036 + 400 Combine like terms: -400 + 400 = 0 0 + x = -331.662479036 + 400 x = -331.662479036 + 400 Combine like terms: -331.662479036 + 400 = 68.337520964 x = 68.337520964 Simplifying x = 68.337520964Solution
The solution to the problem is based on the solutions from the subproblems. x = {731.662479036, 68.337520964}
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