Chapter 4, Problem 15AR

To determine

To solve the given equation, $v^2+25=10v$ by factoring or quadratic formula.

Answer to Problem 15AR

  $x=5$

Explanation of Solution

Given:

The equation is, $v^2+25=10v$

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,

  $\begin{array}{l}{v}^2+25=10v\\ v^2-10v+25=0\end{array}$

Which is in the form of $a{x}^2+bx+c=0$ . Where, $a=1,b=-10\text{ and c = 25}$ .

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

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-\left(-10\right)\pm \sqrt{{\left(-10\right)}^2-4\left(1\right)\left(25\right)}}{2\left(1\right)}\\ x=\frac{10\pm \sqrt{100-100}}{2}\\ x=\frac{10}{2}\\ x=5\end{array}$

Therefore, the root for the given equation, $v^2+25=10v$ is $x=5$ .