What are the solutions to the equation (x^2)/4 =(x+4)/2 ?

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

Find the zeros of (x^2)/4 =(x+4)/2

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

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\frac{x ^{2}}{4} = \frac{x + 4}{2}

x = 4, x = - 2

Solution steps

\frac{x ^{2}}{4} = \frac{x + 4}{2}

Find Least Common Multiplier of

4, 2 : 4

Multiply by LCM=

4

\frac{x ^{2}}{4} \cdot 4 = \frac{x + 4}{2} \cdot 4

Simplify

x^{2} = 2 (x + 4)

Expand

2 (x + 4) : 2 x + 8

x^{2} = 2 x + 8

Move

8

to the left side

x^{2} - 8 = 2 x

Move

2 x

to the left side

x^{2} - 8 - 2 x = 0

Write in the standard form

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

x^{2} - 2 x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( - 8 )}{2 \cdot 1}

(- 2)^{2} - 4 \cdot 1 \cdot (- 8) = 6

x_{1, 2} = \frac{- ( - 2 ) \pm 6}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 6}{2 \cdot 1}, x_{2} = \frac{- ( - 2 ) - 6}{2 \cdot 1}

x = \frac{- ( - 2 ) + 6}{2 \cdot 1} : 4

x = \frac{- ( - 2 ) - 6}{2 \cdot 1} : - 2

The solutions to the quadratic equation are:

x = 4, x = - 2

x - 2 < 12

5 x^{2} + 14 x + 8 = 0

- 4 x^{3} (y - 2) - 32 (2 - y)

4 x^{2} - 32 x + 64

(2 + i)^{2}

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