Question

The square of a number 60 greater than half of the number. Form a

quadratic equation and solve to determine the possible values of the
number.

Answer 1

The number could be
`-7.5` or
`8`.

Explanation:

I'm going to assume this means "The square of a number is 60 greater than half of the number." Let the number be
`x`. The square of
`x` will be
`x^(2)`. "is" denotes that we use the "
`=`" sign, so our equation so far is
`x^(2) =` . Half of
`x` is
`(1)/(2)x`, and "greater than" implies addition, so
`60` greater than
`(1)/(2)x` is
`(1)/(2)x+60`. Therefore, the equation is
`x^(2) =(1)/(2)x+60`.

Solving for
`x`, we get:

`x^(2) =(1)/(2)x+60`

`2x^(2) =x+120` (Multiply both sides of the equation by
`2` to get rid of the fraction)

`2x^(2) -x-120=0` (Subtract
`x+120` from both sides of the equation to make it easier to solve)

`2x^(2) +15x-16x-120=0` (Split
`-x` into
`15x-16x` to make the LHS easier to factor)

`x(2x+15)-8(2x+15)=0` (Take a common factor out of the first two terms and the last two terms)

`(2x+15)(x-8)=0` (Take another common factor out)

`2x+15=0,x-8=0` (Zero Product Property)

`x=-7.5,8` (Solve)

Hope this helps!