What are the solutions to the equation 4.5x=(2x-1)^2 ?

The solutions to the equation 4.5x=(2x-1)^2 are x=2,x= 1/8

Find the zeros of 4.5x=(2x-1)^2

The zeros of 4.5x=(2x-1)^2 are x=2,x= 1/8

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4.5 x = (2 x - 1)^{2}

x = 2, x = \frac{1}{8}

Decimal

x = 2, x = 0.125

Solution steps

4.5 x = (2 x - 1)^{2}

Multiply both sides by

10

45 x = (2 x - 1)^{2} \cdot 10

Expand

(2 x - 1)^{2} \cdot 10 : 40 x^{2} - 40 x + 10

45 x = 40 x^{2} - 40 x + 10

Switch sides

40 x^{2} - 40 x + 10 = 45 x

Move

45 x

to the left side

40 x^{2} - 85 x + 10 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 85 ) \pm ( - 85 ) ^{2} - 4 \cdot 40 \cdot 10}{2 \cdot 40}

(- 85)^{2} - 4 \cdot 40 \cdot 10 = 75

x_{1, 2} = \frac{- ( - 85 ) \pm 75}{2 \cdot 40}

Separate the solutions

x_{1} = \frac{- ( - 85 ) + 75}{2 \cdot 40}, x_{2} = \frac{- ( - 85 ) - 75}{2 \cdot 40}

x = \frac{- ( - 85 ) + 75}{2 \cdot 40} : 2

x = \frac{- ( - 85 ) - 75}{2 \cdot 40} : \frac{1}{8}

The solutions to the quadratic equation are:

x = 2, x = \frac{1}{8}

5 x^{2} - 10 x - 255 = 0

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

x^{2} - 5 x + \frac{9}{4} = 0

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

2 x^{2} + 6 x + 12 = 0

What are the solutions to the equation 4.5x=(2x-1)^2 ?
The solutions to the equation 4.5x=(2x-1)^2 are x=2,x= 1/8
Find the zeros of 4.5x=(2x-1)^2
The zeros of 4.5x=(2x-1)^2 are x=2,x= 1/8