Question

How do you solve $ 5{{r}^{2}}=80 $ using the quadratic formula?

Answer 1

Hint: From the question given it has been asked to solve $ 5{{r}^{2}}=80 $ using the quadratic formula. To solve the given equation by using the quadratic formula we have to get the given equation into the general form of the quadratic equation. We know that general form of the quadratic equation is $ a{{x}^{2}}+bx+c=0 $ and the formulae for obtaining solutions is $ \dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a} $

Complete step by step answer:
From the question, the given equation is $ 5{{r}^{2}}=80 $
Now, move the right-hand side of the equation to the left-hand side of the equation.
By moving the right-hand side of the equation to the left-hand side of the equation, we get
 $ 5{{r}^{2}}-80=0 $
We can clearly observe that it is in the general form of the quadratic equation.
By comparing coefficients of both the equations, we get
 $ \begin{align}
  & a=5 \\
 & b=0 \\
 & c=-80 \\
\end{align} $
Now, it has been asked to solve the equation by using the quadratic formula,
We know that quadratic formula is $ r=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a} $
By using the above formula, we have to solve the obtained quadratic equation.
Substitute the values of coefficients we got in the quadratic formula.
By substituting the values of coefficients, we got in the quadratic formula, we get
 $ r=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a} $
 $ \Rightarrow r=\dfrac{0\pm \sqrt{0-4\left( 5 \right)\left( -80 \right)}}{2\left( 5 \right)} $
 $ \Rightarrow r=\dfrac{0\pm \sqrt{1600}}{10} $
 $ \Rightarrow r=\pm \dfrac{40}{10} $
 $ \Rightarrow r=\pm 4 $
Hence, $ r=\pm 4 $ is the solution for the given question $ 5{{r}^{2}}=80 $ using the quadratic formula.

Note:
We should be well aware of how to transform the given equation into the general form of the quadratic equation. We should be very careful while doing the calculation of the problem, especially while doing the calculation using the quadratic formula. We should be very careful while substituting the values of coefficients in the quadratic formula. This can be also answered in another way but that is not preferable because here we are asked to use the quadratic formula. The other way of solving it is as follows $ 5{{r}^{2}}=80\Rightarrow {{r}^{2}}=16\Rightarrow r=\pm 4 $ .