Chapter 4, Problem 16AR

To determine

To solve the given equation, $x^2=3x+4$ by factoring or quadratic formula.

Answer to Problem 16AR

  $x=4,-1$

Explanation of Solution

Given:

The equation is, $x^2=3x+4$

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,

  $\begin{array}{l}{x}^2=3x+4\\ x^2-3x-4=0\end{array}$

Which is in the form of $a{x}^2+bx+c=0$ . Where, $a=1,b=-3\text{ and c = -4}$ .

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

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-\left(-3\right)\pm \sqrt{{\left(-3\right)}^2-4\left(1\right)\left(-4\right)}}{2\left(1\right)}\\ x=\frac{3\pm \sqrt{9+16}}{2}\\ x=\frac{3\pm \sqrt{25}}{2}\\ x=\frac{3\pm 5}{2}\\ x=\frac{3+5}{2},\frac{3-5}{2}\\ x=\frac{8}{2},\frac{-2}{2}\\ x=4,-1\end{array}$

Therefore, the roots for the given equation, $x^2=3x+4$ are $x=4,-1$ .