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

The solutions to the equation (ax^2)/4+x/2 = 2/a are x= 2/a ,x=-4/a ;\quad a\ne 0

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

The zeros of (ax^2)/4+x/2 = 2/a are x= 2/a ,x=-4/a ;\quad a\ne 0

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

x = \frac{2}{a}, x = - \frac{4}{a}; a \neq = 0

Solution steps

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

Find Least Common Multiplier of

4, 2, a : 4 a

Multiply by LCM=

4 a

\frac{a x ^{2}}{4} \cdot 4 a + \frac{x}{2} \cdot 4 a = \frac{2}{a} \cdot 4 a; a \neq = 0

Simplify

a^{2} x^{2} + 2 a x = 8; a \neq = 0

Move

8

to the left side

a^{2} x^{2} + 2 a x - 8 = 0; a \neq = 0

Solve with the quadratic formula

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

Simplify

(2 a)^{2} - 4 a^{2} (- 8) : 6 a

x_{1, 2} = \frac{- 2 a \pm 6 a}{2 a ^{2}}; a \neq = 0

Separate the solutions

x_{1} = \frac{- 2 a + 6 a}{2 a ^{2}}, x_{2} = \frac{- 2 a - 6 a}{2 a ^{2}}

x = \frac{- 2 a + 6 a}{2 a ^{2}} : \frac{2}{a}

x = \frac{- 2 a - 6 a}{2 a ^{2}} : - \frac{4}{a}

The solutions to the quadratic equation are:

x = \frac{2}{a}, x = - \frac{4}{a}; a \neq = 0

x, 6 x^{2} = 7 x y + 20 y^{2}

5 x^{2} - x^{2} = 2 x^{2} + 72

x, x^{2} + y^{2} - 2 x + 2 y + 11 = 0

(b + 3)^{2} = 25

(x - 2)^{2} + (x - 7)^{2} = x^{2}

What are the solutions to the equation (ax^2)/4+x/2 = 2/a ?
The solutions to the equation (ax^2)/4+x/2 = 2/a are x= 2/a ,x=-4/a ;\quad a\ne 0
Find the zeros of (ax^2)/4+x/2 = 2/a
The zeros of (ax^2)/4+x/2 = 2/a are x= 2/a ,x=-4/a ;\quad a\ne 0