5a-%3D-a2-%E2%88%92-35a.jpeg "(6a − )5a = A2 − 35a")
Solving the Equation: (6a − )5a = a2 − 35a
This article will guide you through the steps to solve the equation (6a − )5a = a2 − 35a. We will simplify the equation and then use algebraic techniques to find the solutions for the variable 'a'.
Step 1: Simplifying the Equation
Firstly, let's address the missing term in the equation. The expression "(6a − )" indicates a multiplication operation, implying there is a missing coefficient or variable to be multiplied by 6a.
Assumption: We will assume the missing term is a simple '1'. This assumption is based on the common occurrence of "1" being a hidden multiplier in algebraic expressions.
The equation becomes: (6a - 1)5a = a2 - 35a
Step 2: Expanding the Left Side
Now we need to distribute the 5a on the left side of the equation:
(6a - 1)5a = 30a2 - 5a
Step 3: Rearranging the Equation
Let's move all terms to one side of the equation to create a quadratic expression:
30a2 - 5a = a2 - 35a
30a2 - a2 - 5a + 35a = 0
29a2 + 30a = 0
Step 4: Factoring the Quadratic Expression
The greatest common factor (GCF) for 29a2 and 30a is 'a'. Factoring out 'a' we get:
a(29a + 30) = 0
Step 5: Solving for 'a'
For the product of two factors to equal zero, at least one of the factors must be zero. Therefore, we have two possible solutions:
- a = 0
- 29a + 30 = 0
Solving the second equation for 'a':
29a = -30 a = -30/29
Conclusion
The solutions to the equation (6a − )5a = a2 − 35a, assuming the missing term is '1', are:
- a = 0
- a = -30/29
Remember, this solution is based on the assumption of '1' being the missing term. If the missing term is different, the solutions will change accordingly.