Question

Solve 4x^2-10x-36=0 using the quadratic formula

Answer 1

Given the equation:

`4x^2-10x-36=0\text{ ---- equation 1}`

To solve using the quadratic formula, we have the solution of the quadratic equation:

`y=ax^2+bx+c\text{ ---- equation 2}`

to be

`x=(-b\pm√(b^2-4ac))/(2a)\text{ ----- equation 3}`

Comparing equations 1 and 2, we have

`\begin{gathered} a=4 \\ b=-10 \\ c=-36 \end{gathered}`

By substituting these values into equation 3, we have

`\begin{gathered} x=(-(-10)\pm√((-10)^2-4(4*-36)))/(2(4)) \\ =(10\pm√(676))/(8) \\ =(10\pm26)/(8) \\ \Rightarrow x=(10+26)/(8)=(9)/(2) \\ or \\ \Rightarrow x=(10-26)/(8)=-2 \end{gathered}`

Hence, the solution, using the quadratic formula, is

`x=(9)/(2)\text{ or x=-2}`