%5E2%2B(x-1)(x%2B1)%3D5(x%2B2)%5E2-(x-5)(x%2B1)%2B(x%2B4)%5E2.jpeg "(2x+3)^2+(x-1)(x+1)=5(x+2)^2-(x-5)(x+1)+(x+4)^2")
Solving the Equation: (2x+3)^2+(x-1)(x+1)=5(x+2)^2-(x-5)(x+1)+(x+4)^2
This article will guide you through the steps involved in solving the given equation:
(2x+3)^2+(x-1)(x+1)=5(x+2)^2-(x-5)(x+1)+(x+4)^2
Let's break down the process step-by-step:
1. Expanding the Expressions:
The first step is to expand all the squared terms and product terms using the appropriate algebraic formulas:
- (a+b)^2 = a^2 + 2ab + b^2
- (a-b)^2 = a^2 - 2ab + b^2
- (a+b)(a-b) = a^2 - b^2
Applying these formulas to our equation, we get:
(4x^2 + 12x + 9) + (x^2 - 1) = 5(x^2 + 4x + 4) - (x^2 - 25) + (x^2 + 8x + 16)
2. Simplifying the Equation:
Now, we need to simplify the equation by removing the parentheses and combining like terms.
4x^2 + 12x + 9 + x^2 - 1 = 5x^2 + 20x + 20 - x^2 + 25 + x^2 + 8x + 16
This simplifies to:
5x^2 + 12x + 8 = 5x^2 + 28x + 61
3. Isolating the Variable:
To solve for x, we need to move all the x terms to one side of the equation and the constant terms to the other.
12x - 28x = 61 - 8
This simplifies to:
-16x = 53
4. Solving for x:
Finally, we can solve for x by dividing both sides of the equation by -16.
x = -53/16
Therefore, the solution to the equation (2x+3)^2+(x-1)(x+1)=5(x+2)^2-(x-5)(x+1)+(x+4)^2 is x = -53/16.