Solve for v. 93v^2 + 78v = 0
Understand the Problem
The question is asking to solve for the variable 'v' in the quadratic equation 93v^2 + 78v = 0. To solve this, we can factor out a common term and then set each factor equal to zero to find the possible values of 'v'.
Answer
$v = 0, -\frac{26}{31}$
Answer for screen readers
$v = 0, -\frac{26}{31}$
Steps to Solve
- Factor out the common term
The common term in the equation $93v^2 + 78v = 0$ is $v$. Factoring out $v$ gives us:
$v(93v + 78) = 0$
- Set each factor equal to zero
Now, we set each factor equal to zero and solve for $v$:
$v = 0$ or $93v + 78 = 0$
- Solve for v in the second equation
Subtract 78 from both sides:
$93v = -78$
Divide both sides by 93:
$v = -\frac{78}{93}$
- Simplify the fraction
Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 3:
$v = -\frac{78 \div 3}{93 \div 3} = -\frac{26}{31}$
$v = 0, -\frac{26}{31}$
More Information
The solutions to the quadratic equation $93v^2 + 78v = 0$ are $v = 0$ and $v = -\frac{26}{31}$.
Tips
A common mistake is forgetting to factor out the variable $v$ completely, or only finding one solution. Remember that quadratic equations can have up to two solutions. In this case, factoring helps to find both values of $v$ that satisfy the equation.
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