What are the solutions to the equation (x-3)^2= x/4 ?

The solutions to the equation (x-3)^2= x/4 are x=4,x= 9/4

Find the zeros of (x-3)^2= x/4

The zeros of (x-3)^2= x/4 are x=4,x= 9/4

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(x - 3)^{2} = \frac{x}{4}

x = 4, x = \frac{9}{4}

Decimal Notation

x = 4, x = 2.25

Solution steps

(x - 3)^{2} = \frac{x}{4}

Multiply both sides by

4

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

Expand

4 (x - 3)^{2} : 4 x^{2} - 24 x + 36

4 x^{2} - 24 x + 36 = x

Move

x

to the left side

4 x^{2} - 25 x + 36 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 25 ) \pm ( - 25 ) ^{2} - 4 \cdot 4 \cdot 36}{2 \cdot 4}

(- 25)^{2} - 4 \cdot 4 \cdot 36 = 7

x_{1, 2} = \frac{- ( - 25 ) \pm 7}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 25 ) + 7}{2 \cdot 4}, x_{2} = \frac{- ( - 25 ) - 7}{2 \cdot 4}

x = \frac{- ( - 25 ) + 7}{2 \cdot 4} : 4

x = \frac{- ( - 25 ) - 7}{2 \cdot 4} : \frac{9}{4}

The solutions to the quadratic equation are:

x = 4, x = \frac{9}{4}

x (x + 8) = 48

7 x^{2} - 27 x - 4 = 0

24 x^{2} - 18 x = 0

6 x - x^{2} = 9

x, y = x^{2} y

What are the solutions to the equation (x-3)^2= x/4 ?
The solutions to the equation (x-3)^2= x/4 are x=4,x= 9/4
Find the zeros of (x-3)^2= x/4
The zeros of (x-3)^2= x/4 are x=4,x= 9/4