What are the solutions to the equation (x^2)/8-x/4 = 1/2 ?

The solutions to the equation (x^2)/8-x/4 = 1/2 are x=1+sqrt(5),x=1-sqrt(5)

Find the zeros of (x^2)/8-x/4 = 1/2

The zeros of (x^2)/8-x/4 = 1/2 are x=1+sqrt(5),x=1-sqrt(5)

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\frac{x ^{2}}{8} - \frac{x}{4} = \frac{1}{2}

x = 1 + 5, x = 1 - 5

Decimal Notation

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

Solution steps

\frac{x ^{2}}{8} - \frac{x}{4} = \frac{1}{2}

Find Least Common Multiplier of

8, 4, 2 : 8

Multiply by LCM=

8

\frac{x ^{2}}{8} \cdot 8 - \frac{x}{4} \cdot 8 = \frac{1}{2} \cdot 8

Simplify

x^{2} - 2 x = 4

Move

4

to the left side

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

m^{2} + 8 m = - 16

0 = - 2 x^{2}

3 3^{2} + 4 4^{2} = c^{2}

4.3 \cdot 1 0^{- 7} = \frac{x ^{2}}{0.05}

(2 x - 3) (x + 5) = 0

What are the solutions to the equation (x^2)/8-x/4 = 1/2 ?
The solutions to the equation (x^2)/8-x/4 = 1/2 are x=1+sqrt(5),x=1-sqrt(5)
Find the zeros of (x^2)/8-x/4 = 1/2
The zeros of (x^2)/8-x/4 = 1/2 are x=1+sqrt(5),x=1-sqrt(5)