What are the solutions to the equation x(x-3)=5x+1 ?

The solutions to the equation x(x-3)=5x+1 are x=4+sqrt(17),x=4-sqrt(17)

Find the zeros of x(x-3)=5x+1

The zeros of x(x-3)=5x+1 are x=4+sqrt(17),x=4-sqrt(17)

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x (x - 3) = 5 x + 1

x = 4 + 17, x = 4 - 17

Decimal Notation

x = 8.12310 \dots, x = - 0.12310 \dots

Solution steps

x (x - 3) = 5 x + 1

Expand

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

x^{2} - 3 x = 5 x + 1

Move

1

to the left side

x^{2} - 3 x - 1 = 5 x

Move

5 x

to the left side

x^{2} - 8 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

(- 8)^{2} - 4 \cdot 1 \cdot (- 1) = 217

x_{1, 2} = \frac{- ( - 8 ) \pm 2 17}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 2 17}{2 \cdot 1}, x_{2} = \frac{- ( - 8 ) - 2 17}{2 \cdot 1}

x = \frac{- ( - 8 ) + 2 17}{2 \cdot 1} : 4 + 17

x = \frac{- ( - 8 ) - 2 17}{2 \cdot 1} : 4 - 17

The solutions to the quadratic equation are:

x = 4 + 17, x = 4 - 17

x^{2} - 4 x + 1 = 0

0 = - 4.9 t^{2} + 19.6 t + 58.8

x, x^{2} - 6 x + 10 = 0

289 = x^{2}

x^{2} + 3 x - 19 = 0

What are the solutions to the equation x(x-3)=5x+1 ?
The solutions to the equation x(x-3)=5x+1 are x=4+sqrt(17),x=4-sqrt(17)
Find the zeros of x(x-3)=5x+1
The zeros of x(x-3)=5x+1 are x=4+sqrt(17),x=4-sqrt(17)