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Simplifying 6.14x2 + 4875040.95x + 350000000 = 0 Reorder the terms: 350000000 + 4875040.95x + 6.14x2 = 0 Solving 350000000 + 4875040.95x + 6.14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.14 the coefficient of the squared term: Divide each side by '6.14'. 57003257.33 + 793980.6107x + x2 = 0 Move the constant term to the right: Add '-57003257.33' to each side of the equation. 57003257.33 + 793980.6107x + -57003257.33 + x2 = 0 + -57003257.33 Reorder the terms: 57003257.33 + -57003257.33 + 793980.6107x + x2 = 0 + -57003257.33 Combine like terms: 57003257.33 + -57003257.33 = 0.00 0.00 + 793980.6107x + x2 = 0 + -57003257.33 793980.6107x + x2 = 0 + -57003257.33 Combine like terms: 0 + -57003257.33 = -57003257.33 793980.6107x + x2 = -57003257.33 The x term is 793980.6107x. Take half its coefficient (396990.3054). Square it (157601302600) and add it to both sides. Add '157601302600' to each side of the equation. 793980.6107x + 157601302600 + x2 = -57003257.33 + 157601302600 Reorder the terms: 157601302600 + 793980.6107x + x2 = -57003257.33 + 157601302600 Combine like terms: -57003257.33 + 157601302600 = 157544299342.67 157601302600 + 793980.6107x + x2 = 157544299342.67 Factor a perfect square on the left side: (x + 396990.3054)(x + 396990.3054) = 157544299342.67 Calculate the square root of the right side: 396918.504661436 Break this problem into two subproblems by setting (x + 396990.3054) equal to 396918.504661436 and -396918.504661436.Subproblem 1
x + 396990.3054 = 396918.504661436 Simplifying x + 396990.3054 = 396918.504661436 Reorder the terms: 396990.3054 + x = 396918.504661436 Solving 396990.3054 + x = 396918.504661436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-396990.3054' to each side of the equation. 396990.3054 + -396990.3054 + x = 396918.504661436 + -396990.3054 Combine like terms: 396990.3054 + -396990.3054 = 0.0000 0.0000 + x = 396918.504661436 + -396990.3054 x = 396918.504661436 + -396990.3054 Combine like terms: 396918.504661436 + -396990.3054 = -71.800738564 x = -71.800738564 Simplifying x = -71.800738564Subproblem 2
x + 396990.3054 = -396918.504661436 Simplifying x + 396990.3054 = -396918.504661436 Reorder the terms: 396990.3054 + x = -396918.504661436 Solving 396990.3054 + x = -396918.504661436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-396990.3054' to each side of the equation. 396990.3054 + -396990.3054 + x = -396918.504661436 + -396990.3054 Combine like terms: 396990.3054 + -396990.3054 = 0.0000 0.0000 + x = -396918.504661436 + -396990.3054 x = -396918.504661436 + -396990.3054 Combine like terms: -396918.504661436 + -396990.3054 = -793908.810061436 x = -793908.810061436 Simplifying x = -793908.810061436Solution
The solution to the problem is based on the solutions from the subproblems. x = {-71.800738564, -793908.810061436}
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