Question

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

${\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{5}\mathbf{=}\mathbf{-}\mathbf{3}\mathit{x}$

Short answer

The solutions of the equation are $\mathbf{-}\mathbf{4}\mathbf{.2}\mathbf{\&}\mathbf{1}\mathbf{.2}$.

Step-by-step solution

Step 1. Graph the equation.

Graph theequation$x^2-5=-3x$ to find the roots.

Step 2. State the interpretation of the graph.

In the graph of the equation,$x^2-5=-3x$ it can be observed that the x-intercepts appear to be at$-4.193\&1.193$, therefore, the solutions to the nearest tenth are $-4.2\&1.2$

Step 3. Check the solutions.

To check the solutions, use the quadratic formula.

$x^2+bx+c=0,\text{then\hspace{0.17em}\hspace{0.17em}}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\begin{array}{l}{x}^2+3x-5=0;a=1,b=3,c=-5\\ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-3\pm \sqrt{3^2-4\left(1\right)(-5)}}{2\left(1\right)}\\ =\frac{-3\pm \sqrt{29}}{2}\\ x=\frac{-3-\sqrt{29}}{2}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}x=\frac{-3+\sqrt{29}}{2}\\ x=-4.192\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}x=1.192\end{array}$

Thus, the solutions are (nearest tenth): $-4.2\&1.2$.