What are the solutions to the equation x^2-1/4 = 1/5 (x/4-1) ?

The solutions to the equation x^2-1/4 = 1/5 (x/4-1) are x= 1/4 ,x=-1/5

Find the zeros of x^2-1/4 = 1/5 (x/4-1)

The zeros of x^2-1/4 = 1/5 (x/4-1) are x= 1/4 ,x=-1/5

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x^{2} - \frac{1}{4} = \frac{1}{5} (\frac{x}{4} - 1)

x = \frac{1}{4}, x = - \frac{1}{5}

Decimal Notation

x = 0.25, x = - 0.2

Solution steps

x^{2} - \frac{1}{4} = \frac{1}{5} (\frac{x}{4} - 1)

Find Least Common Multiplier of

4, 5 : 20

Multiply by LCM=

20

x^{2} \cdot 20 - \frac{1}{4} \cdot 20 = \frac{1}{5} (\frac{x}{4} - 1) \cdot 20

Simplify

20 x^{2} - 5 = 4 (\frac{x}{4} - 1)

Expand

4 (\frac{x}{4} - 1) : x - 4

20 x^{2} - 5 = x - 4

Move

4

to the left side

20 x^{2} - 1 = x

Move

x

to the left side

20 x^{2} - 1 - x = 0

Write in the standard form

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

20 x^{2} - x - 1 = 0

Solve with the quadratic formula

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

(- 1)^{2} - 4 \cdot 20 (- 1) = 9

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

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 9}{2 \cdot 20}, x_{2} = \frac{- ( - 1 ) - 9}{2 \cdot 20}

x = \frac{- ( - 1 ) + 9}{2 \cdot 20} : \frac{1}{4}

x = \frac{- ( - 1 ) - 9}{2 \cdot 20} : - \frac{1}{5}

The solutions to the quadratic equation are:

x = \frac{1}{4}, x = - \frac{1}{5}

- 5 x^{2} - 2 x - 1 = 0

15 c + 12 (- 16 c - 11)

x - 2 > 4 - x

- 2 (0) - 3

n^{2} + 10 n - 45 = 0

What are the solutions to the equation x^2-1/4 = 1/5 (x/4-1) ?
The solutions to the equation x^2-1/4 = 1/5 (x/4-1) are x= 1/4 ,x=-1/5
Find the zeros of x^2-1/4 = 1/5 (x/4-1)
The zeros of x^2-1/4 = 1/5 (x/4-1) are x= 1/4 ,x=-1/5