%E2%88%92(x2%E2%88%9227x)%3Dax2%2Bbx.jpeg "(8x2−15x)−(x2−27x)=ax2+bx")
Solving a Quadratic Equation: (8x²−15x)−(x2−27x)=ax²+bx
This article will guide you through solving the quadratic equation (8x²−15x)−(x2−27x)=ax²+bx and finding the values of a and b.
Step 1: Simplify the Equation
First, we need to simplify the equation by removing the parentheses and combining like terms:
(8x²−15x)−(x²−27x) = 8x² - 15x - x² + 27x = 7x² + 12x
Therefore, the simplified equation becomes: 7x² + 12x = ax² + bx
Step 2: Matching Coefficients
Now, we need to match the coefficients of the corresponding terms on both sides of the equation:
- Coefficients of x²: 7 = a
- Coefficients of x: 12 = b
Step 3: Solution
We have now determined the values of a and b:
- a = 7
- b = 12
Therefore, the solution to the equation is: (8x²−15x)−(x2−27x)=7x² + 12x
Conclusion
By simplifying the equation and matching the coefficients, we were able to solve for the values of a and b. This process demonstrates how to manipulate algebraic expressions to achieve a desired outcome.