Question

Solve by using the Quadratic Formula:$b^2+24=-10b$

Short answer

The solution of the above equation is$b=-4$and$b=-6$

Step-by-step solution

Given information

We are given an quadratic equation$b^2+24=-10b$

Write the equation in standard form by adding 10bto each side. and identify the values of x,y,z

We get,

$b^2+10b+24=0$

On comparing with standard form we get

$x=1,y=10,z=24$

Write quadratic formula and substitute the values of x,y,z

The quadratic formula can be given as

$b=\frac{-y\pm \sqrt{y^2-4xz}}{2x}$

Now we substitute the values of $x,y,z$

We get,role="math" localid="1644928858295" $b=\frac{-10\pm \sqrt{100-4\left(24\right)}}{2}$

Simplify and find the values of b

We get

$$\begin{gathered} b=\frac{-10\pm \sqrt{100-4\left(24\right)}}{2} \\ b=\frac{-10\pm \sqrt{100-96}}{2} \\ b=\frac{-10\pm 2}{2} \end{gathered}$$

$$\begin{gathered} b=\frac{-10\pm \sqrt{100-4\left(24\right)}}{2} \\ b=\frac{-10\pm \sqrt{100-96}}{2} \\ b=\frac{-10\pm 2}{2} \end{gathered}$$

On further simplifying we get

$$\begin{gathered} b=\frac{-10+2}{2} \\ b=\frac{-8}{2} \\ b=-4 \end{gathered}$$and$$\begin{gathered} b=\frac{-10-2}{2} \\ b=\frac{-12}{2} \\ b=-6 \end{gathered}$$

Check the solution

We substitute $x=-4$in the quadratic equation

$$\begin{gathered} b^2+10b+24 \\ {(-4)}^2+10(-4)+24 \\ 16-40+24 \\ =0 \end{gathered}$$

Now we substitute $x=-6$in the quadratic equation

$$\begin{gathered} b^2+10b+24 \\ {(-6)}^2+10(-6)+24 \\ 36-60+24 \\ =0 \end{gathered}$$

Conclusion

The solution of the above equation is$b=-4$and$b=-6$