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Simplifying 151.725x2 + 6181.2x + -309060 = 0 Reorder the terms: -309060 + 6181.2x + 151.725x2 = 0 Solving -309060 + 6181.2x + 151.725x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 151.725 the coefficient of the squared term: Divide each side by '151.725'. -2036.97479 + 40.7394958x + x2 = 0 Move the constant term to the right: Add '2036.97479' to each side of the equation. -2036.97479 + 40.7394958x + 2036.97479 + x2 = 0 + 2036.97479 Reorder the terms: -2036.97479 + 2036.97479 + 40.7394958x + x2 = 0 + 2036.97479 Combine like terms: -2036.97479 + 2036.97479 = 0.00000 0.00000 + 40.7394958x + x2 = 0 + 2036.97479 40.7394958x + x2 = 0 + 2036.97479 Combine like terms: 0 + 2036.97479 = 2036.97479 40.7394958x + x2 = 2036.97479 The x term is 40.7394958x. Take half its coefficient (20.3697479). Square it (414.9266295) and add it to both sides. Add '414.9266295' to each side of the equation. 40.7394958x + 414.9266295 + x2 = 2036.97479 + 414.9266295 Reorder the terms: 414.9266295 + 40.7394958x + x2 = 2036.97479 + 414.9266295 Combine like terms: 2036.97479 + 414.9266295 = 2451.9014195 414.9266295 + 40.7394958x + x2 = 2451.9014195 Factor a perfect square on the left side: (x + 20.3697479)(x + 20.3697479) = 2451.9014195 Calculate the square root of the right side: 49.516678195 Break this problem into two subproblems by setting (x + 20.3697479) equal to 49.516678195 and -49.516678195.Subproblem 1
x + 20.3697479 = 49.516678195 Simplifying x + 20.3697479 = 49.516678195 Reorder the terms: 20.3697479 + x = 49.516678195 Solving 20.3697479 + x = 49.516678195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.3697479' to each side of the equation. 20.3697479 + -20.3697479 + x = 49.516678195 + -20.3697479 Combine like terms: 20.3697479 + -20.3697479 = 0.0000000 0.0000000 + x = 49.516678195 + -20.3697479 x = 49.516678195 + -20.3697479 Combine like terms: 49.516678195 + -20.3697479 = 29.146930295 x = 29.146930295 Simplifying x = 29.146930295Subproblem 2
x + 20.3697479 = -49.516678195 Simplifying x + 20.3697479 = -49.516678195 Reorder the terms: 20.3697479 + x = -49.516678195 Solving 20.3697479 + x = -49.516678195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.3697479' to each side of the equation. 20.3697479 + -20.3697479 + x = -49.516678195 + -20.3697479 Combine like terms: 20.3697479 + -20.3697479 = 0.0000000 0.0000000 + x = -49.516678195 + -20.3697479 x = -49.516678195 + -20.3697479 Combine like terms: -49.516678195 + -20.3697479 = -69.886426095 x = -69.886426095 Simplifying x = -69.886426095Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.146930295, -69.886426095}
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