Question

How do you solve $5{{v}^{2}}-7v=1$ using the quadratic formula?

Answer 1

Hint: Here in this question we have been asked to solve the given quadratic expression $5{{v}^{2}}-7v=1$ using the quadratic formula. From the basic concepts we know that the formula for finding the roots of a quadratic expression in the form of $a{{x}^{2}}+bx+c=0$ is generally given as $\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ .

Complete step by step solution:
Now considering from the question we have been asked to solve the given quadratic expression $5{{v}^{2}}-7v=1$ using the quadratic formula.
From the basic concepts we know that the formula for finding the roots of a quadratic expression in the form of $a{{x}^{2}}+bx+c=0$ is generally given as $\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ .
Here for the given expression $a=5,b=-7,c=-1$ . By applying the formula we will have $\dfrac{-\left( -7 \right)\pm \sqrt{{{\left( -7 \right)}^{2}}-4\left( 5 \right)\left( -1 \right)}}{2\left( 5 \right)}$ .
Now by further simplifying this expression we will have $ \dfrac{7\pm \sqrt{49+20}}{10}$ .
If we simplify this further then we will have $ \dfrac{7\pm \sqrt{69}}{10}$ .
Therefore we can conclude that the solutions of the given quadratic expression $5{{v}^{2}}-7v=1$ will be given as $\dfrac{7\pm \sqrt{69}}{10}$ .

Note: During the process of answering questions of this type we should be careful with the calculations that we are performing in between the steps and the concepts that we are going to apply. This is a very simple and easy question and can be answered accurately in a short span of time. Very few mistakes are possible in questions of this type. Someone can make a calculation mistake and consider it as $ \dfrac{7\pm \sqrt{49}}{10}=\dfrac{7\pm 7}{10}=0,1.4$ then they will end up having a wrong conclusion.