Question

Write the following equations as quadratics in standard form (with = 0). Make sure to remove any brackets and fractions present.

Question 1:

`(x)/(2) = x^2 - (3)/(2)`

Question 2:

`(5)/(x) + 1 = x`

Answer 1

`-2x^2+x+3=0`

`-x^2+x+5=0`

Explanation:

Algebraic Manipulation

Consists of applying basic rules of algebra to simplify or transform algebraic expressions into others.

We are required to rewrite two expressions as quadratics in standard form.

Question 1:

`\displaystyle (x)/(2) = x^2 - (3)/(2)`

To get rid of the denominators, multiply by 2:

`x=2x^2-3`

Move all the terms to the left side:

`x-2x^2+3=0`

Order by degree:

`\boxed{-2x^2+x+3=0}`

Question 2:

`\displaystyle (5)/(x) + 1 = x`

Multiply by x (x must be different from 0):

`5+x=x^2`

Move all the terms to the left side:

`5+x-x^2=0`

Order by degree:

`\boxed{-x^2+x+5=0}`