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

The solutions to the equation (x^2)/4-x/2-1=0 are x=1+sqrt(5),x=1-sqrt(5)

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

The zeros of (x^2)/4-x/2-1=0 are x=1+sqrt(5),x=1-sqrt(5)

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

x = 1 + 5, x = 1 - 5

Decimal Notation

x = 3.23606 \dots, x = - 1.23606 \dots

Solution steps

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

Find Least Common Multiplier of

4, 2 : 4

Multiply by LCM=

4

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

Simplify

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

Solve with the quadratic formula

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

(- 2)^{2} - 4 \cdot 1 \cdot (- 4) = 25

x_{1, 2} = \frac{- ( - 2 ) \pm 2 5}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 5}{2 \cdot 1}, x_{2} = \frac{- ( - 2 ) - 2 5}{2 \cdot 1}

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

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

The solutions to the quadratic equation are:

x = 1 + 5, x = 1 - 5

x (3 x + 10) = 77

1^{2} + x^{2} = 8^{2}

2 x^{2} + 36 = 6 x

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

(x - 4)^{2} = 19

What are the solutions to the equation (x^2)/4-x/2-1=0 ?
The solutions to the equation (x^2)/4-x/2-1=0 are x=1+sqrt(5),x=1-sqrt(5)
Find the zeros of (x^2)/4-x/2-1=0
The zeros of (x^2)/4-x/2-1=0 are x=1+sqrt(5),x=1-sqrt(5)