How do you solve {x^2} - 3 = 0 using the quadratic formula?

To solve the equation x² - 3 = 0 using the quadratic formula, follow these steps:

Write the equation in standard form:
The quadratic formula applies to equations in the form ax² + bx + c = 0.
Your equation is x² - 3 = 0.
This can be rewritten as:
x² + 0x - 3 = 0.
Here, a = 1, b = 0, and c = -3.

Apply the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / 2a.

Substitute the values of a, b, and c into the formula:
For your equation, a = 1, b = 0, and c = -3.
Substitute these values into the quadratic formula:
x = [-(0) ± √(0² - 4(1)(-3))] / (2(1))
x = [0 ± √(0 + 12)] / 2
x = [0 ± √12] / 2

Simplify the square root:
√12 can be simplified as √(4 * 3) = 2√3.

Final simplification:
Now the equation becomes:
x = [0 ± 2√3] / 2.
Simplifying further, we get:
x = ±√3.

Thus, the solutions to the equation x² - 3 = 0 are:
x = √3 and x = -√3.