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

The solutions to the equation x(-5+x)=3 are x=(5+sqrt(37))/2 ,x=(5-sqrt(37))/2

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

The zeros of x(-5+x)=3 are x=(5+sqrt(37))/2 ,x=(5-sqrt(37))/2

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x (- 5 + x) = 3

x = \frac{5 + 37}{2}, x = \frac{5 - 37}{2}

Decimal Notation

x = 5.54138 \dots, x = - 0.54138 \dots

Solution steps

x (- 5 + x) = 3

Expand

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

- 5 x + x^{2} = 3

Move

3

to the left side

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

Write in the standard form

a x^{2} + b x + c = 0

x^{2} - 5 x - 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 1 \cdot ( - 3 )}{2 \cdot 1}

(- 5)^{2} - 4 \cdot 1 \cdot (- 3) = 37

x_{1, 2} = \frac{- ( - 5 ) \pm 37}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 37}{2 \cdot 1}, x_{2} = \frac{- ( - 5 ) - 37}{2 \cdot 1}

x = \frac{- ( - 5 ) + 37}{2 \cdot 1} : \frac{5 + 37}{2}

x = \frac{- ( - 5 ) - 37}{2 \cdot 1} : \frac{5 - 37}{2}

The solutions to the quadratic equation are:

x = \frac{5 + 37}{2}, x = \frac{5 - 37}{2}

7 x^{2} = 7

x, x^{2} - 9 y^{2} + 2 x - 54 y = 80

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

- 4 x^{2} - 40 x - 280 = 0

- 2 x^{2} + 2 x + 12 = 0

What are the solutions to the equation x(-5+x)=3 ?
The solutions to the equation x(-5+x)=3 are x=(5+sqrt(37))/2 ,x=(5-sqrt(37))/2
Find the zeros of x(-5+x)=3
The zeros of x(-5+x)=3 are x=(5+sqrt(37))/2 ,x=(5-sqrt(37))/2