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

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

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

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

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

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

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

Multiply both sides by

4

4 x (1 - x) = 1

Expand

4 x (1 - x) : 4 x - 4 x^{2}

4 x - 4 x^{2} = 1

Move

1

to the left side

4 x - 4 x^{2} - 1 = 0

Write in the standard form

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

- 4 x^{2} + 4 x - 1 = 0

Solve with the quadratic formula

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

4^{2} - 4 (- 4) (- 1) = 0

x_{1, 2} = \frac{- 4 \pm 0}{2 ( - 4 )}

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

\frac{- 4}{2 ( - 4 )} = \frac{1}{2}

x = \frac{1}{2}

The solution to the quadratic equation is:

x = \frac{1}{2}

1 = 5 + ∣ 2 - 3 x ∣

3 b^{2} - 2 b - 5

x > \frac{1}{x}

0 = \frac{1609}{75} + 2 (- 5.929) x

3^{2} + 5^{2} = x^{2}

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