What are the solutions to the equation (x-5)^2+3(x-5)+9=0 ?

The solutions to the equation (x-5)^2+3(x-5)+9=0 are x= 7/2+i(3sqrt(3))/2 ,x= 7/2-i(3sqrt(3))/2

Find the zeros of (x-5)^2+3(x-5)+9=0

The zeros of (x-5)^2+3(x-5)+9=0 are x= 7/2+i(3sqrt(3))/2 ,x= 7/2-i(3sqrt(3))/2

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(x - 5)^{2} + 3 (x - 5) + 9 = 0

x = \frac{7}{2} + i \frac{3 3}{2}, x = \frac{7}{2} - i \frac{3 3}{2}

Solution steps

(x - 5)^{2} + 3 (x - 5) + 9 = 0

Expand

(x - 5)^{2} + 3 (x - 5) + 9 : x^{2} - 7 x + 19

x^{2} - 7 x + 19 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 1 \cdot 19}{2 \cdot 1}

Simplify

(- 7)^{2} - 4 \cdot 1 \cdot 19 : 33 i

x_{1, 2} = \frac{- ( - 7 ) \pm 3 3 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 7 ) + 3 3 i}{2 \cdot 1}, x_{2} = \frac{- ( - 7 ) - 3 3 i}{2 \cdot 1}

x = \frac{- ( - 7 ) + 3 3 i}{2 \cdot 1} : \frac{7}{2} + i \frac{3 3}{2}

x = \frac{- ( - 7 ) - 3 3 i}{2 \cdot 1} : \frac{7}{2} - i \frac{3 3}{2}

The solutions to the quadratic equation are:

x = \frac{7}{2} + i \frac{3 3}{2}, x = \frac{7}{2} - i \frac{3 3}{2}

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

- 3 (x + 2)^{2} = - 18

0.8 \cdot 5

(x + 5)^{2} = 49

\frac{3}{3} + \frac{3}{3}

What are the solutions to the equation (x-5)^2+3(x-5)+9=0 ?
The solutions to the equation (x-5)^2+3(x-5)+9=0 are x= 7/2+i(3sqrt(3))/2 ,x= 7/2-i(3sqrt(3))/2
Find the zeros of (x-5)^2+3(x-5)+9=0
The zeros of (x-5)^2+3(x-5)+9=0 are x= 7/2+i(3sqrt(3))/2 ,x= 7/2-i(3sqrt(3))/2