What are the solutions to the equation 2x(x-2)=9 ?

The solutions to the equation 2x(x-2)=9 are x=(2+sqrt(22))/2 ,x=(2-sqrt(22))/2

Find the zeros of 2x(x-2)=9

The zeros of 2x(x-2)=9 are x=(2+sqrt(22))/2 ,x=(2-sqrt(22))/2

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2 x (x - 2) = 9

x = \frac{2 + 22}{2}, x = \frac{2 - 22}{2}

Decimal Notation

x = 3.34520 \dots, x = - 1.34520 \dots

Solution steps

2 x (x - 2) = 9

Expand

2 x (x - 2) : 2 x^{2} - 4 x

2 x^{2} - 4 x = 9

Move

9

to the left side

2 x^{2} - 4 x - 9 = 0

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 2 (- 9) = 222

x_{1, 2} = \frac{- ( - 4 ) \pm 2 22}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 22}{2 \cdot 2}, x_{2} = \frac{- ( - 4 ) - 2 22}{2 \cdot 2}

x = \frac{- ( - 4 ) + 2 22}{2 \cdot 2} : \frac{2 + 22}{2}

x = \frac{- ( - 4 ) - 2 22}{2 \cdot 2} : \frac{2 - 22}{2}

The solutions to the quadratic equation are:

x = \frac{2 + 22}{2}, x = \frac{2 - 22}{2}

x^{2} - 6 x - 8 = 0

x^{2} + 2 x - 99 = 0

4 v^{2} + 4 = 40

(32 - x)^{2} + (16 - x)^{2} = x^{2}

5 x^{2} + 40 x = - 75

What are the solutions to the equation 2x(x-2)=9 ?
The solutions to the equation 2x(x-2)=9 are x=(2+sqrt(22))/2 ,x=(2-sqrt(22))/2
Find the zeros of 2x(x-2)=9
The zeros of 2x(x-2)=9 are x=(2+sqrt(22))/2 ,x=(2-sqrt(22))/2