2%3D6x%2B9.jpeg "(x-5)2=6x+9")
(x-5)² = 6x + 9: A Quadratic Equation
In mathematics, quadratic equations are polynomial equations of degree two, which means the highest power of the variable (usually x) is two. In this article, we will discuss the quadratic equation (x-5)² = 6x + 9.
Understanding the Equation
The given equation is (x-5)² = 6x + 9. To understand this equation, let's break it down:
- (x-5)² is the square of (x-5), which means we need to multiply (x-5) by itself.
- The equation states that the result of this multiplication is equal to 6x + 9.
Expanding the Equation
To solve this equation, we need to expand the left-hand side of the equation:
(x-5)² = x² - 10x + 25
So, the equation becomes:
x² - 10x + 25 = 6x + 9
Rearranging the Terms
Rearrange the terms to get all the variables on one side of the equation:
x² - 16x + 16 = 0
Factoring the Quadratic
The quadratic equation can be factored as:
(x - 8)(x - 2) = 0
Solving for x
To find the solutions, we set each factor equal to zero:
x - 8 = 0 => x = 8
x - 2 = 0 => x = 2
Conclusion
Therefore, the solutions to the equation (x-5)² = 6x + 9 are x = 2 and x = 8. In conclusion, we have successfully solved the quadratic equation and found its solutions.
