What are the solutions to the equation (2x-3)^2=8x ?

The solutions to the equation (2x-3)^2=8x are x= 9/2 ,x= 1/2

Find the zeros of (2x-3)^2=8x

The zeros of (2x-3)^2=8x are x= 9/2 ,x= 1/2

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(2 x - 3)^{2} = 8 x

x = \frac{9}{2}, x = \frac{1}{2}

Decimal Notation

x = 4.5, x = 0.5

Solution steps

(2 x - 3)^{2} = 8 x

Expand

(2 x - 3)^{2} : 4 x^{2} - 12 x + 9

4 x^{2} - 12 x + 9 = 8 x

Move

8 x

to the left side

4 x^{2} - 20 x + 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 20 ) \pm ( - 20 ) ^{2} - 4 \cdot 4 \cdot 9}{2 \cdot 4}

(- 20)^{2} - 4 \cdot 4 \cdot 9 = 16

x_{1, 2} = \frac{- ( - 20 ) \pm 16}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 20 ) + 16}{2 \cdot 4}, x_{2} = \frac{- ( - 20 ) - 16}{2 \cdot 4}

x = \frac{- ( - 20 ) + 16}{2 \cdot 4} : \frac{9}{2}

x = \frac{- ( - 20 ) - 16}{2 \cdot 4} : \frac{1}{2}

The solutions to the quadratic equation are:

x = \frac{9}{2}, x = \frac{1}{2}

7 y - 10 = y^{2}

12 x^{2} - 280 x + 1200 = 0

3 x^{2} + 17 = - 10 x + 9

2 z^{2} - 1 = 0

a^{2} = 5 a

What are the solutions to the equation (2x-3)^2=8x ?
The solutions to the equation (2x-3)^2=8x are x= 9/2 ,x= 1/2
Find the zeros of (2x-3)^2=8x
The zeros of (2x-3)^2=8x are x= 9/2 ,x= 1/2