(x%2B1)-(x-3)%5E2%3D(3x-5)(3x%2B5)-(3x%2B1)%5E2%2B(x-2)%5E2-x%5E2.jpeg "(x-7)(x+1)-(x-3)^2=(3x-5)(3x+5)-(3x+1)^2+(x-2)^2-x^2")
Solving a Complex Algebraic Expression
In this article, we will solve the following complex algebraic expression:
$(x-7)(x+1)-(x-3)^2=(3x-5)(3x+5)-(3x+1)^2+(x-2)^2-x^2$
Step 1: Expand the Left-Hand Side
Let's start by expanding the left-hand side of the equation:
$(x-7)(x+1)-(x-3)^2=x^2-6x-7-(x^2-6x+9)$
Simplifying the expression, we get:
$-14=-x^2+12x-9$
Step 2: Expand the Right-Hand Side
Now, let's expand the right-hand side of the equation:
$(3x-5)(3x+5)-(3x+1)^2+(x-2)^2-x^2=9x^2-25-(9x^2+6x+1)+(x^2-4x+4)-x^2$
Simplifying the expression, we get:
$-26=-2x^2-10x+4$
Step 3: Equate the Two Expressions
Now that we have expanded both sides of the equation, we can equate them:
$-14=-2x^2-10x+4$
Step 4: Solve for x
Rearranging the equation, we get:
$2x^2+10x-18=0$
Factoring the quadratic equation, we get:
$(x+6)(2x-3)=0$
Solving for x, we get:
$x=-6, x=\frac{3}{2}$
Therefore, the solutions to the equation are x = -6 and x = 3/2.
Conclusion
In this article, we have solved the complex algebraic expression $(x-7)(x+1)-(x-3)^2=(3x-5)(3x+5)-(3x+1)^2+(x-2)^2-x^2$ to find the values of x that satisfy the equation.
