%5E2%3D3.jpeg "(x-1)^2=3")
Solving the Equation (x-1)^2 = 3
This equation is a quadratic equation in disguise. Let's break down how to solve it:
1. Expanding the Equation
First, expand the left side of the equation:
(x - 1)^2 = (x - 1)(x - 1) = x^2 - 2x + 1
Now we have: x^2 - 2x + 1 = 3
2. Rearranging the Equation
To solve the quadratic equation, we need to set it equal to zero:
x^2 - 2x - 2 = 0
3. Solving the Quadratic Equation
We can solve this equation using the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / 2a
Where a = 1, b = -2, and c = -2.
Plugging in the values:
x = [2 ± √((-2)^2 - 4 * 1 * -2)] / (2 * 1)
x = [2 ± √(12)] / 2
x = [2 ± 2√3] / 2
4. Simplifying the Solution
Finally, we can simplify the solution:
x = 1 ± √3
Therefore, the solutions to the equation (x-1)^2 = 3 are:
x = 1 + √3 and x = 1 - √3