** Resolve the Equation: 5(2x-3)^2 - 5(x+1)^2 - 15(x+4)(x-4) = -10 **
In this article, we will solve the equation 5(2x-3)^2 - 5(x+1)^2 - 15(x+4)(x-4) = -10. This equation involves quadratic expressions and requires some algebraic manipulations to arrive at the solution.
Step 1: Expand the Quadratic Expressions
First, let's expand the quadratic expressions in the equation:
5(2x-3)^2 = 5(4x^2 - 12x + 9) = 20x^2 - 60x + 45
-5(x+1)^2 = -5(x^2 + 2x + 1) = -5x^2 - 10x - 5
Now, substitute these expansions back into the equation:
20x^2 - 60x + 45 - 5x^2 - 10x - 5 - 15(x+4)(x-4) = -10
Step 2: Simplify the Equation
Next, simplify the equation by combining like terms:
15x^2 - 70x + 40 - 15(x^2 - 16) = -10
Step 3: Expand and Simplify the Remaining Expression
Now, expand and simplify the remaining expression:
15x^2 - 70x + 40 - 15x^2 + 240 = -10
Combine like terms:
-70x + 280 = -10
Step 4: Solve for x
Finally, solve for x:
-70x = -290
x = 290/70
x = 29/7
Therefore, the solution to the equation 5(2x-3)^2 - 5(x+1)^2 - 15(x+4)(x-4) = -10 is x = 29/7.
