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Simplifying 1000 = 150x + -3x2 Solving 1000 = 150x + -3x2 Solving for variable 'x'. Reorder the terms: 1000 + -150x + 3x2 = 150x + -150x + -3x2 + 3x2 Combine like terms: 150x + -150x = 0 1000 + -150x + 3x2 = 0 + -3x2 + 3x2 1000 + -150x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 1000 + -150x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 333.3333333 + -50x + x2 = 0 Move the constant term to the right: Add '-333.3333333' to each side of the equation. 333.3333333 + -50x + -333.3333333 + x2 = 0 + -333.3333333 Reorder the terms: 333.3333333 + -333.3333333 + -50x + x2 = 0 + -333.3333333 Combine like terms: 333.3333333 + -333.3333333 = 0.0000000 0.0000000 + -50x + x2 = 0 + -333.3333333 -50x + x2 = 0 + -333.3333333 Combine like terms: 0 + -333.3333333 = -333.3333333 -50x + x2 = -333.3333333 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -333.3333333 + 625 Reorder the terms: 625 + -50x + x2 = -333.3333333 + 625 Combine like terms: -333.3333333 + 625 = 291.6666667 625 + -50x + x2 = 291.6666667 Factor a perfect square on the left side: (x + -25)(x + -25) = 291.6666667 Calculate the square root of the right side: 17.078251278 Break this problem into two subproblems by setting (x + -25) equal to 17.078251278 and -17.078251278.Subproblem 1
x + -25 = 17.078251278 Simplifying x + -25 = 17.078251278 Reorder the terms: -25 + x = 17.078251278 Solving -25 + x = 17.078251278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 17.078251278 + 25 Combine like terms: -25 + 25 = 0 0 + x = 17.078251278 + 25 x = 17.078251278 + 25 Combine like terms: 17.078251278 + 25 = 42.078251278 x = 42.078251278 Simplifying x = 42.078251278Subproblem 2
x + -25 = -17.078251278 Simplifying x + -25 = -17.078251278 Reorder the terms: -25 + x = -17.078251278 Solving -25 + x = -17.078251278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -17.078251278 + 25 Combine like terms: -25 + 25 = 0 0 + x = -17.078251278 + 25 x = -17.078251278 + 25 Combine like terms: -17.078251278 + 25 = 7.921748722 x = 7.921748722 Simplifying x = 7.921748722Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.078251278, 7.921748722}
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