Question

Identify the values of a, b, and c that could be used with the quadratic formula to solve the equation. Enter a as a positive integer value. x^2=4(x-9)

Answer 1

Given the following equation:

`x^2=4(x-9)`

First of all, we note that the quadratic equation is written in the general form shown below;

`ax^2+bx+c=0`

We shall now attempt to re-write the equation given in the form shown above. This is shown as follows;

`\begin{gathered} x^2=4(x-9)_{} \\ We\text{ shall now expand the parenthesis;} \\ x^2=4x-36 \\ We\text{ shall now collect all like terms;} \\ \text{Subtract 4x and add 36 to both sides to both sides} \end{gathered}`
`\begin{gathered} x^2-4x+36=4x-4x-36+36 \\ x^2-4x+36=0 \end{gathered}`

We now have our quadratic equation as shown above.

Comparing this with the general form of a quadratic equation, we can now identify a, b and c as follows;

`\begin{gathered} a=1 \\ b=-4 \\ c=36 \end{gathered}`

ANSWER:

a = 1

b = -4 and

c = 36