What are the solutions to the equation -1/4 x^2+1/2 x+1/2 =0 ?

The solutions to the equation -1/4 x^2+1/2 x+1/2 =0 are x=1-sqrt(3),x=1+sqrt(3)

Find the zeros of -1/4 x^2+1/2 x+1/2 =0

The zeros of -1/4 x^2+1/2 x+1/2 =0 are x=1-sqrt(3),x=1+sqrt(3)

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

x = 1 - 3, x = 1 + 3

Decimal Notation

x = - 0.73205 \dots, x = 2.73205 \dots

Solution steps

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

Find Least Common Multiplier of

4, 2 : 4

Multiply by LCM=

4

- \frac{1}{4} x^{2} \cdot 4 + \frac{1}{2} x \cdot 4 + \frac{1}{2} \cdot 4 = 0 \cdot 4

Simplify

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

Solve with the quadratic formula

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

2^{2} - 4 (- 1) \cdot 2 = 23

x_{1, 2} = \frac{- 2 \pm 2 3}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 2 + 2 3}{2 ( - 1 )}, x_{2} = \frac{- 2 - 2 3}{2 ( - 1 )}

x = \frac{- 2 + 2 3}{2 ( - 1 )} : 1 - 3

x = \frac{- 2 - 2 3}{2 ( - 1 )} : 1 + 3

The solutions to the quadratic equation are:

x = 1 - 3, x = 1 + 3

12 x^{2} - 6 x = 0

7 X^{2} = 98

(x + 9)^{2} = 121

(x - 2)^{2} - 43 = 21

7 x^{2} = 98

What are the solutions to the equation -1/4 x^2+1/2 x+1/2 =0 ?
The solutions to the equation -1/4 x^2+1/2 x+1/2 =0 are x=1-sqrt(3),x=1+sqrt(3)
Find the zeros of -1/4 x^2+1/2 x+1/2 =0
The zeros of -1/4 x^2+1/2 x+1/2 =0 are x=1-sqrt(3),x=1+sqrt(3)