Chapter 9, Problem 12MCQ

To determine

Solve the equation $x^2=12$ by graphing

Answer to Problem 12MCQ

The solutions are (nearest tenth): $x=3.5\text{or}x=-3.5$

Explanation of Solution

Given:

The equation: $x^2=12$

Concept Used:

The equation: $x^2=12$

Rewrite the equation in standard form: $x^2-12=0$

Calculation:

Graph the equation: $x^2-12=0$

The x − intercepts of the graph appear to be at − 3.464 and 3.464. So the solutions are (nearest tenth): − 3.5 and 3.5.

  $\begin{array}{c}a{x}^2+bx+c=0,\text{then}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x^2-12=0\\ a=1b=0;c=-12\\ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-0\pm \sqrt{0^2-4·1·-12}}{2·1}=\frac{\pm \sqrt{48}}{2}=\pm \frac{4\sqrt{3}}{2}\\ x=\frac{4\sqrt{3}}{2}\text{and}-\frac{4\sqrt{3}}{2}\\ x=2\sqrt{3}\text{and}-2\sqrt{3}\\ x=3.464\text{and}-3.464\\ x\approx 3.5\text{and}x\approx -3.5\end{array}$

Now estimate the result to nearest tenth: $x=3.5\text{or}x=-3.5$

Thus, the solutions are (nearest tenth): $x=3.5\text{or}x=-3.5$