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Simplifying 0.3214x2 + -4.6571x + 30.6x = 30.6 Reorder the terms: -4.6571x + 30.6x + 0.3214x2 = 30.6 Combine like terms: -4.6571x + 30.6x = 25.9429x 25.9429x + 0.3214x2 = 30.6 Solving 25.9429x + 0.3214x2 = 30.6 Solving for variable 'x'. Reorder the terms: -30.6 + 25.9429x + 0.3214x2 = 30.6 + -30.6 Combine like terms: 30.6 + -30.6 = 0.0 -30.6 + 25.9429x + 0.3214x2 = 0.0 Begin completing the square. Divide all terms by 0.3214 the coefficient of the squared term: Divide each side by '0.3214'. -95.20846297 + 80.71841942x + x2 = 0 Move the constant term to the right: Add '95.20846297' to each side of the equation. -95.20846297 + 80.71841942x + 95.20846297 + x2 = 0 + 95.20846297 Reorder the terms: -95.20846297 + 95.20846297 + 80.71841942x + x2 = 0 + 95.20846297 Combine like terms: -95.20846297 + 95.20846297 = 0.00000000 0.00000000 + 80.71841942x + x2 = 0 + 95.20846297 80.71841942x + x2 = 0 + 95.20846297 Combine like terms: 0 + 95.20846297 = 95.20846297 80.71841942x + x2 = 95.20846297 The x term is 80.71841942x. Take half its coefficient (40.35920971). Square it (1628.865808) and add it to both sides. Add '1628.865808' to each side of the equation. 80.71841942x + 1628.865808 + x2 = 95.20846297 + 1628.865808 Reorder the terms: 1628.865808 + 80.71841942x + x2 = 95.20846297 + 1628.865808 Combine like terms: 95.20846297 + 1628.865808 = 1724.07427097 1628.865808 + 80.71841942x + x2 = 1724.07427097 Factor a perfect square on the left side: (x + 40.35920971)(x + 40.35920971) = 1724.07427097 Calculate the square root of the right side: 41.521973351 Break this problem into two subproblems by setting (x + 40.35920971) equal to 41.521973351 and -41.521973351.Subproblem 1
x + 40.35920971 = 41.521973351 Simplifying x + 40.35920971 = 41.521973351 Reorder the terms: 40.35920971 + x = 41.521973351 Solving 40.35920971 + x = 41.521973351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.35920971' to each side of the equation. 40.35920971 + -40.35920971 + x = 41.521973351 + -40.35920971 Combine like terms: 40.35920971 + -40.35920971 = 0.00000000 0.00000000 + x = 41.521973351 + -40.35920971 x = 41.521973351 + -40.35920971 Combine like terms: 41.521973351 + -40.35920971 = 1.162763641 x = 1.162763641 Simplifying x = 1.162763641Subproblem 2
x + 40.35920971 = -41.521973351 Simplifying x + 40.35920971 = -41.521973351 Reorder the terms: 40.35920971 + x = -41.521973351 Solving 40.35920971 + x = -41.521973351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.35920971' to each side of the equation. 40.35920971 + -40.35920971 + x = -41.521973351 + -40.35920971 Combine like terms: 40.35920971 + -40.35920971 = 0.00000000 0.00000000 + x = -41.521973351 + -40.35920971 x = -41.521973351 + -40.35920971 Combine like terms: -41.521973351 + -40.35920971 = -81.881183061 x = -81.881183061 Simplifying x = -81.881183061Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.162763641, -81.881183061}
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