(8x2−15x)−(x2−27x)=ax2+bx

2 min read Jun 16, 2024
(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.

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