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Simplifying 804200 = 0.08x2 + -13.08x + 927 Reorder the terms: 804200 = 927 + -13.08x + 0.08x2 Solving 804200 = 927 + -13.08x + 0.08x2 Solving for variable 'x'. Combine like terms: 804200 + -927 = 803273 803273 + 13.08x + -0.08x2 = 927 + -13.08x + 0.08x2 + -927 + 13.08x + -0.08x2 Reorder the terms: 803273 + 13.08x + -0.08x2 = 927 + -927 + -13.08x + 13.08x + 0.08x2 + -0.08x2 Combine like terms: 927 + -927 = 0 803273 + 13.08x + -0.08x2 = 0 + -13.08x + 13.08x + 0.08x2 + -0.08x2 803273 + 13.08x + -0.08x2 = -13.08x + 13.08x + 0.08x2 + -0.08x2 Combine like terms: -13.08x + 13.08x = 0.00 803273 + 13.08x + -0.08x2 = 0.00 + 0.08x2 + -0.08x2 803273 + 13.08x + -0.08x2 = 0.08x2 + -0.08x2 Combine like terms: 0.08x2 + -0.08x2 = 0.00 803273 + 13.08x + -0.08x2 = 0.00 Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. -10040912.5 + -163.5x + x2 = 0 Move the constant term to the right: Add '10040912.5' to each side of the equation. -10040912.5 + -163.5x + 10040912.5 + x2 = 0 + 10040912.5 Reorder the terms: -10040912.5 + 10040912.5 + -163.5x + x2 = 0 + 10040912.5 Combine like terms: -10040912.5 + 10040912.5 = 0.0 0.0 + -163.5x + x2 = 0 + 10040912.5 -163.5x + x2 = 0 + 10040912.5 Combine like terms: 0 + 10040912.5 = 10040912.5 -163.5x + x2 = 10040912.5 The x term is -163.5x. Take half its coefficient (-81.75). Square it (6683.0625) and add it to both sides. Add '6683.0625' to each side of the equation. -163.5x + 6683.0625 + x2 = 10040912.5 + 6683.0625 Reorder the terms: 6683.0625 + -163.5x + x2 = 10040912.5 + 6683.0625 Combine like terms: 10040912.5 + 6683.0625 = 10047595.5625 6683.0625 + -163.5x + x2 = 10047595.5625 Factor a perfect square on the left side: (x + -81.75)(x + -81.75) = 10047595.5625 Calculate the square root of the right side: 3169.794246083 Break this problem into two subproblems by setting (x + -81.75) equal to 3169.794246083 and -3169.794246083.Subproblem 1
x + -81.75 = 3169.794246083 Simplifying x + -81.75 = 3169.794246083 Reorder the terms: -81.75 + x = 3169.794246083 Solving -81.75 + x = 3169.794246083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81.75' to each side of the equation. -81.75 + 81.75 + x = 3169.794246083 + 81.75 Combine like terms: -81.75 + 81.75 = 0.00 0.00 + x = 3169.794246083 + 81.75 x = 3169.794246083 + 81.75 Combine like terms: 3169.794246083 + 81.75 = 3251.544246083 x = 3251.544246083 Simplifying x = 3251.544246083Subproblem 2
x + -81.75 = -3169.794246083 Simplifying x + -81.75 = -3169.794246083 Reorder the terms: -81.75 + x = -3169.794246083 Solving -81.75 + x = -3169.794246083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81.75' to each side of the equation. -81.75 + 81.75 + x = -3169.794246083 + 81.75 Combine like terms: -81.75 + 81.75 = 0.00 0.00 + x = -3169.794246083 + 81.75 x = -3169.794246083 + 81.75 Combine like terms: -3169.794246083 + 81.75 = -3088.044246083 x = -3088.044246083 Simplifying x = -3088.044246083Solution
The solution to the problem is based on the solutions from the subproblems. x = {3251.544246083, -3088.044246083}
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