Chapter 4, Problem 18AR

To determine

To solve the given equation, $y^2=20y-36$ by factoring or quadratic formula.

Answer to Problem 18AR

  $x=18,x=2$

Explanation of Solution

Given:

The equation is, $y^2=20y-36$

Calculation:

We can solve the given equation by using quadratic formula.

That is,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Now, write the equation as,

  $\begin{array}{l}{y}^2=20y-36\\ y^2-20y+36=0\end{array}$

Which is in the form of $a{x}^2+bx+c=0$ . Where, $a=1,b=-20\text{ and c = 36}$ .

Now, Substitute the values in the formula then we get that,

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-\left(-20\right)\pm \sqrt{{\left(-20\right)}^2-4\left(1\right)\left(36\right)}}{2\left(1\right)}\\ x=\frac{20\pm \sqrt{400-144}}{2}\\ x=\frac{20\pm \sqrt{256}}{2}\\ x=\frac{20\pm 16}{2}\\ x=\frac{20+16}{2},x=\frac{20-16}{2}\\ x=\frac{36}{2},x=\frac{4}{2}\\ x=18,x=2\end{array}$

Therefore, the roots for the given equation, $y^2=20y-36$ are $x=18,x=2$ .