2%3D(x%2B1)2-quadratic-equation.jpeg "(2x-1)2=(x+1)2 Quadratic Equation")
Solving the Quadratic Equation: (2x-1)² = (x+1)²
In this article, we will explore a quadratic equation of the form (2x-1)² = (x+1)² and learn how to solve it.
What is a Quadratic Equation?
A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (in this case, x) is two. It has the general form of:
ax² + bx + c = 0
where a, b, and c are constants.
Simplifying the Equation
Let's start by expanding both sides of the equation using the exponent rule (a+b)² = a² + 2ab + b²:
(2x-1)² = (x+1)²
4x² - 4x + 1 = x² + 2x + 1
Moving All Terms to One Side
Our goal is to set one side of the equation to zero, so let's move all terms to the left side:
4x² - 4x + 1 - x² - 2x - 1 = 0
3x² - 6x = 0
Factoring the Equation
Now, let's try to factor the left side of the equation:
3x(x - 2) = 0
Solving for x
This tells us that either 3x = 0 or x - 2 = 0. Solving for x, we get:
x = 0 or x = 2
Therefore, the solutions to the quadratic equation (2x-1)² = (x+1)² are x = 0 and x = 2.
Conclusion
In this article, we have successfully solved the quadratic equation (2x-1)² = (x+1)² using the exponent rule, simplification, and factoring. We found that the solutions to the equation are x = 0 and x = 2. I hope this helps you understand how to solve quadratic equations!
