What are the solutions to the equation (x-1)(x-4)=-5 ?

The solutions to the equation (x-1)(x-4)=-5 are x= 5/2+i(sqrt(11))/2 ,x= 5/2-i(sqrt(11))/2

Find the zeros of (x-1)(x-4)=-5

The zeros of (x-1)(x-4)=-5 are x= 5/2+i(sqrt(11))/2 ,x= 5/2-i(sqrt(11))/2

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(x - 1) (x - 4) = - 5

x = \frac{5}{2} + i \frac{11}{2}, x = \frac{5}{2} - i \frac{11}{2}

Solution steps

(x - 1) (x - 4) = - 5

Expand

(x - 1) (x - 4) : x^{2} - 5 x + 4

x^{2} - 5 x + 4 = - 5

Move

5

to the left side

x^{2} - 5 x + 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 1 \cdot 9}{2 \cdot 1}

Simplify

(- 5)^{2} - 4 \cdot 1 \cdot 9 : 11 i

x_{1, 2} = \frac{- ( - 5 ) \pm 11 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 11 i}{2 \cdot 1}, x_{2} = \frac{- ( - 5 ) - 11 i}{2 \cdot 1}

x = \frac{- ( - 5 ) + 11 i}{2 \cdot 1} : \frac{5}{2} + i \frac{11}{2}

x = \frac{- ( - 5 ) - 11 i}{2 \cdot 1} : \frac{5}{2} - i \frac{11}{2}

The solutions to the quadratic equation are:

x = \frac{5}{2} + i \frac{11}{2}, x = \frac{5}{2} - i \frac{11}{2}

4 (2 x - 7) - 3 (3 x + 1) = 2 - (7 - x)

- (2 x^{5})^{3}

- 12 x - 38 < - 200

5 = - \frac{1}{3} (x - 9)

0.695 = 0.004 x + 0.01933

What are the solutions to the equation (x-1)(x-4)=-5 ?
The solutions to the equation (x-1)(x-4)=-5 are x= 5/2+i(sqrt(11))/2 ,x= 5/2-i(sqrt(11))/2
Find the zeros of (x-1)(x-4)=-5
The zeros of (x-1)(x-4)=-5 are x= 5/2+i(sqrt(11))/2 ,x= 5/2-i(sqrt(11))/2