(x%2B6)-(2x-3)(x-1)%3D6-x%5E2.jpeg "(x-6)(x+6)-(2x-3)(x-1)=6-x^2")
Solving the Algebraic Expression: (x-6)(x+6)-(2x-3)(x-1)=6-x^2
In this article, we will solve the algebraic expression (x-6)(x+6)-(2x-3)(x-1)=6-x^2 and explore the steps to simplify the equation.
Step 1: Expand the Expression
First, let's expand the given expression:
(x-6)(x+6) = x^2 - 36 ... (1)
(2x-3)(x-1) = 2x^2 - 5x + 3 ... (2)
Now, let's substitute equations (1) and (2) into the original expression:
x^2 - 36 - (2x^2 - 5x + 3) = 6 - x^2
Step 2: Simplify the Expression
Next, let's simplify the expression by combining like terms:
x^2 - 36 - 2x^2 + 5x - 3 = 6 - x^2
-x^2 + 5x - 39 = 6 - x^2
Step 3: Rearrange the Terms
Now, let's rearrange the terms to get a simpler form:
2x^2 - 5x + 45 = 0
Conclusion
In conclusion, we have successfully simplified the algebraic expression (x-6)(x+6)-(2x-3)(x-1)=6-x^2 to 2x^2 - 5x + 45 = 0. This quadratic equation can be solved further to find the roots of the equation.
