What are the solutions to the equation 2(x-4)+3x-x^2=3 ?

The solutions to the equation 2(x-4)+3x-x^2=3 are x= 5/2-i(sqrt(19))/2 ,x= 5/2+i(sqrt(19))/2

Find the zeros of 2(x-4)+3x-x^2=3

The zeros of 2(x-4)+3x-x^2=3 are x= 5/2-i(sqrt(19))/2 ,x= 5/2+i(sqrt(19))/2

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2 (x - 4) + 3 x - x^{2} = 3

x = \frac{5}{2} - i \frac{19}{2}, x = \frac{5}{2} + i \frac{19}{2}

Solution steps

2 (x - 4) + 3 x - x^{2} = 3

Expand

2 (x - 4) + 3 x - x^{2} : - x^{2} + 5 x - 8

- x^{2} + 5 x - 8 = 3

Move

3

to the left side

- x^{2} + 5 x - 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 ( - 1 ) ( - 11 )}{2 ( - 1 )}

Simplify

5^{2} - 4 (- 1) (- 11) : 19 i

x_{1, 2} = \frac{- 5 \pm 19 i}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 5 + 19 i}{2 ( - 1 )}, x_{2} = \frac{- 5 - 19 i}{2 ( - 1 )}

x = \frac{- 5 + 19 i}{2 ( - 1 )} : \frac{5}{2} - i \frac{19}{2}

x = \frac{- 5 - 19 i}{2 ( - 1 )} : \frac{5}{2} + i \frac{19}{2}

The solutions to the quadratic equation are:

x = \frac{5}{2} - i \frac{19}{2}, x = \frac{5}{2} + i \frac{19}{2}

- 8 \leq 1 - 3 (x - 2) < 13

(1 - 0.537) = \frac{x}{\frac{500}{0.55} + 100.02}

\frac{m ^{- 6} n ^{- 3}}{m ^{- 13} n ^{- 1}}

\frac{x ^{2}}{4} = \frac{x + 4}{2}

x - 2 < 12

What are the solutions to the equation 2(x-4)+3x-x^2=3 ?
The solutions to the equation 2(x-4)+3x-x^2=3 are x= 5/2-i(sqrt(19))/2 ,x= 5/2+i(sqrt(19))/2
Find the zeros of 2(x-4)+3x-x^2=3
The zeros of 2(x-4)+3x-x^2=3 are x= 5/2-i(sqrt(19))/2 ,x= 5/2+i(sqrt(19))/2