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Simplifying -3870 = 0.1x2 + 50x Reorder the terms: -3870 = 50x + 0.1x2 Solving -3870 = 50x + 0.1x2 Solving for variable 'x'. Reorder the terms: -3870 + -50x + -0.1x2 = 50x + -50x + 0.1x2 + -0.1x2 Combine like terms: 50x + -50x = 0 -3870 + -50x + -0.1x2 = 0 + 0.1x2 + -0.1x2 -3870 + -50x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -3870 + -50x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 38700 + 500x + x2 = 0 Move the constant term to the right: Add '-38700' to each side of the equation. 38700 + 500x + -38700 + x2 = 0 + -38700 Reorder the terms: 38700 + -38700 + 500x + x2 = 0 + -38700 Combine like terms: 38700 + -38700 = 0 0 + 500x + x2 = 0 + -38700 500x + x2 = 0 + -38700 Combine like terms: 0 + -38700 = -38700 500x + x2 = -38700 The x term is 500x. Take half its coefficient (250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. 500x + 62500 + x2 = -38700 + 62500 Reorder the terms: 62500 + 500x + x2 = -38700 + 62500 Combine like terms: -38700 + 62500 = 23800 62500 + 500x + x2 = 23800 Factor a perfect square on the left side: (x + 250)(x + 250) = 23800 Calculate the square root of the right side: 154.272486205 Break this problem into two subproblems by setting (x + 250) equal to 154.272486205 and -154.272486205.Subproblem 1
x + 250 = 154.272486205 Simplifying x + 250 = 154.272486205 Reorder the terms: 250 + x = 154.272486205 Solving 250 + x = 154.272486205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 154.272486205 + -250 Combine like terms: 250 + -250 = 0 0 + x = 154.272486205 + -250 x = 154.272486205 + -250 Combine like terms: 154.272486205 + -250 = -95.727513795 x = -95.727513795 Simplifying x = -95.727513795Subproblem 2
x + 250 = -154.272486205 Simplifying x + 250 = -154.272486205 Reorder the terms: 250 + x = -154.272486205 Solving 250 + x = -154.272486205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = -154.272486205 + -250 Combine like terms: 250 + -250 = 0 0 + x = -154.272486205 + -250 x = -154.272486205 + -250 Combine like terms: -154.272486205 + -250 = -404.272486205 x = -404.272486205 Simplifying x = -404.272486205Solution
The solution to the problem is based on the solutions from the subproblems. x = {-95.727513795, -404.272486205}
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