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Simplifying -0.02x2 + 33x + -4200 = 0 Reorder the terms: -4200 + 33x + -0.02x2 = 0 Solving -4200 + 33x + -0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 210000 + -1650x + x2 = 0 Move the constant term to the right: Add '-210000' to each side of the equation. 210000 + -1650x + -210000 + x2 = 0 + -210000 Reorder the terms: 210000 + -210000 + -1650x + x2 = 0 + -210000 Combine like terms: 210000 + -210000 = 0 0 + -1650x + x2 = 0 + -210000 -1650x + x2 = 0 + -210000 Combine like terms: 0 + -210000 = -210000 -1650x + x2 = -210000 The x term is -1650x. Take half its coefficient (-825). Square it (680625) and add it to both sides. Add '680625' to each side of the equation. -1650x + 680625 + x2 = -210000 + 680625 Reorder the terms: 680625 + -1650x + x2 = -210000 + 680625 Combine like terms: -210000 + 680625 = 470625 680625 + -1650x + x2 = 470625 Factor a perfect square on the left side: (x + -825)(x + -825) = 470625 Calculate the square root of the right side: 686.021136701 Break this problem into two subproblems by setting (x + -825) equal to 686.021136701 and -686.021136701.Subproblem 1
x + -825 = 686.021136701 Simplifying x + -825 = 686.021136701 Reorder the terms: -825 + x = 686.021136701 Solving -825 + x = 686.021136701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '825' to each side of the equation. -825 + 825 + x = 686.021136701 + 825 Combine like terms: -825 + 825 = 0 0 + x = 686.021136701 + 825 x = 686.021136701 + 825 Combine like terms: 686.021136701 + 825 = 1511.021136701 x = 1511.021136701 Simplifying x = 1511.021136701Subproblem 2
x + -825 = -686.021136701 Simplifying x + -825 = -686.021136701 Reorder the terms: -825 + x = -686.021136701 Solving -825 + x = -686.021136701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '825' to each side of the equation. -825 + 825 + x = -686.021136701 + 825 Combine like terms: -825 + 825 = 0 0 + x = -686.021136701 + 825 x = -686.021136701 + 825 Combine like terms: -686.021136701 + 825 = 138.978863299 x = 138.978863299 Simplifying x = 138.978863299Solution
The solution to the problem is based on the solutions from the subproblems. x = {1511.021136701, 138.978863299}
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