Question

If the equation x2 + 8x - 4 = 2x - 7 is written in the form (x + 5)2 + t = 0, what is the value of t?

Answer 1

We have the equation:

`x^2+8x-4=2x-7`

We have to compare it to the equation:

`(x+s)^2+t=0`

We start by rearranging the first equation:

`\begin{gathered} x^2+8x-4=2x-7 \\ x^2+8x-2x-4+7=0 \\ x^2+6x+3=0 \end{gathered}`

We then add a term to find the square in order to factorize it as the second equation:

`\begin{gathered} x^2+6x+3=0 \\ x^2+2(3x)+3^2-3^2+3=0 \\ (x+3)^2-9+3=0 \\ (x+3)^2-6=0 \end{gathered}`

Then, comparing to the second equation, s = 3 and t = -6.

Answer: the value of t for this quadratic equation is t = -6.