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Simplifying 19.5x2 + -357x + 1156 = 0 Reorder the terms: 1156 + -357x + 19.5x2 = 0 Solving 1156 + -357x + 19.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19.5 the coefficient of the squared term: Divide each side by '19.5'. 59.28205128 + -18.30769231x + x2 = 0 Move the constant term to the right: Add '-59.28205128' to each side of the equation. 59.28205128 + -18.30769231x + -59.28205128 + x2 = 0 + -59.28205128 Reorder the terms: 59.28205128 + -59.28205128 + -18.30769231x + x2 = 0 + -59.28205128 Combine like terms: 59.28205128 + -59.28205128 = 0.00000000 0.00000000 + -18.30769231x + x2 = 0 + -59.28205128 -18.30769231x + x2 = 0 + -59.28205128 Combine like terms: 0 + -59.28205128 = -59.28205128 -18.30769231x + x2 = -59.28205128 The x term is -18.30769231x. Take half its coefficient (-9.153846155). Square it (83.79289943) and add it to both sides. Add '83.79289943' to each side of the equation. -18.30769231x + 83.79289943 + x2 = -59.28205128 + 83.79289943 Reorder the terms: 83.79289943 + -18.30769231x + x2 = -59.28205128 + 83.79289943 Combine like terms: -59.28205128 + 83.79289943 = 24.51084815 83.79289943 + -18.30769231x + x2 = 24.51084815 Factor a perfect square on the left side: (x + -9.153846155)(x + -9.153846155) = 24.51084815 Calculate the square root of the right side: 4.950843176 Break this problem into two subproblems by setting (x + -9.153846155) equal to 4.950843176 and -4.950843176.Subproblem 1
x + -9.153846155 = 4.950843176 Simplifying x + -9.153846155 = 4.950843176 Reorder the terms: -9.153846155 + x = 4.950843176 Solving -9.153846155 + x = 4.950843176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.153846155' to each side of the equation. -9.153846155 + 9.153846155 + x = 4.950843176 + 9.153846155 Combine like terms: -9.153846155 + 9.153846155 = 0.000000000 0.000000000 + x = 4.950843176 + 9.153846155 x = 4.950843176 + 9.153846155 Combine like terms: 4.950843176 + 9.153846155 = 14.104689331 x = 14.104689331 Simplifying x = 14.104689331Subproblem 2
x + -9.153846155 = -4.950843176 Simplifying x + -9.153846155 = -4.950843176 Reorder the terms: -9.153846155 + x = -4.950843176 Solving -9.153846155 + x = -4.950843176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.153846155' to each side of the equation. -9.153846155 + 9.153846155 + x = -4.950843176 + 9.153846155 Combine like terms: -9.153846155 + 9.153846155 = 0.000000000 0.000000000 + x = -4.950843176 + 9.153846155 x = -4.950843176 + 9.153846155 Combine like terms: -4.950843176 + 9.153846155 = 4.203002979 x = 4.203002979 Simplifying x = 4.203002979Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.104689331, 4.203002979}
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