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Simplifying 0.03x2 + -33x + 15000 = 13000 Reorder the terms: 15000 + -33x + 0.03x2 = 13000 Solving 15000 + -33x + 0.03x2 = 13000 Solving for variable 'x'. Reorder the terms: 15000 + -13000 + -33x + 0.03x2 = 13000 + -13000 Combine like terms: 15000 + -13000 = 2000 2000 + -33x + 0.03x2 = 13000 + -13000 Combine like terms: 13000 + -13000 = 0 2000 + -33x + 0.03x2 = 0 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. 66666.66667 + -1100x + x2 = 0 Move the constant term to the right: Add '-66666.66667' to each side of the equation. 66666.66667 + -1100x + -66666.66667 + x2 = 0 + -66666.66667 Reorder the terms: 66666.66667 + -66666.66667 + -1100x + x2 = 0 + -66666.66667 Combine like terms: 66666.66667 + -66666.66667 = 0.00000 0.00000 + -1100x + x2 = 0 + -66666.66667 -1100x + x2 = 0 + -66666.66667 Combine like terms: 0 + -66666.66667 = -66666.66667 -1100x + x2 = -66666.66667 The x term is -1100x. Take half its coefficient (-550). Square it (302500) and add it to both sides. Add '302500' to each side of the equation. -1100x + 302500 + x2 = -66666.66667 + 302500 Reorder the terms: 302500 + -1100x + x2 = -66666.66667 + 302500 Combine like terms: -66666.66667 + 302500 = 235833.33333 302500 + -1100x + x2 = 235833.33333 Factor a perfect square on the left side: (x + -550)(x + -550) = 235833.33333 Calculate the square root of the right side: 485.626742808 Break this problem into two subproblems by setting (x + -550) equal to 485.626742808 and -485.626742808.Subproblem 1
x + -550 = 485.626742808 Simplifying x + -550 = 485.626742808 Reorder the terms: -550 + x = 485.626742808 Solving -550 + x = 485.626742808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '550' to each side of the equation. -550 + 550 + x = 485.626742808 + 550 Combine like terms: -550 + 550 = 0 0 + x = 485.626742808 + 550 x = 485.626742808 + 550 Combine like terms: 485.626742808 + 550 = 1035.626742808 x = 1035.626742808 Simplifying x = 1035.626742808Subproblem 2
x + -550 = -485.626742808 Simplifying x + -550 = -485.626742808 Reorder the terms: -550 + x = -485.626742808 Solving -550 + x = -485.626742808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '550' to each side of the equation. -550 + 550 + x = -485.626742808 + 550 Combine like terms: -550 + 550 = 0 0 + x = -485.626742808 + 550 x = -485.626742808 + 550 Combine like terms: -485.626742808 + 550 = 64.373257192 x = 64.373257192 Simplifying x = 64.373257192Solution
The solution to the problem is based on the solutions from the subproblems. x = {1035.626742808, 64.373257192}
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