-(x%5E2-27x)%3Dax%5E2%2Bbx.jpeg "(8x^2-15x)-(x^2-27x)=ax^2+bx")
Solving the Equation: (8x^2 - 15x) - (x^2 - 27x) = ax^2 + bx
This article will guide you through the steps to solve the given equation and determine the values of 'a' and 'b'.
1. Simplify the Left Side of the Equation
First, we need to simplify the left side of the equation by distributing the negative sign and combining like terms:
(8x^2 - 15x) - (x^2 - 27x) = 8x^2 - 15x - x^2 + 27x = 7x^2 + 12x
2. Matching Coefficients
Now, we have:
7x^2 + 12x = ax^2 + bx
To find the values of 'a' and 'b', we simply need to match the coefficients of the corresponding terms on both sides of the equation:
- Coefficient of x^2: 7 = a
- Coefficient of x: 12 = b
3. Solution
Therefore, the solution is:
- a = 7
- b = 12
By simplifying the expression and comparing coefficients, we have successfully solved the equation and found the values for 'a' and 'b'.