The quadratic equation x^2 - 6x + 4 = 0 can be solved using the quadratic formula, where the coefficients are a = 1, b = -6, and c = 4. The solutions are x = √5 + 3 or x = -√5 + 3.
We can solve the equation using the quadratic formula, which is a general formula for solving quadratic equations.
Rearrange terms:
-3x + 4 = -x^2 + 3x
Move terms to the left side:
-3x + 4 - (-x^2 + 3x) = 0
Distribute:
-3x + 4 + x^2 - 3x = 0
Combine like terms:
x^2 - 6x + 4 = 0
Use the quadratic formula:
Where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -6, and c = 4. Substituting these values into the formula, we get:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = -6, and c = 4. Substituting these values into the formula:
x = (6 ± √((-6)^2 - 4 * 1 * 4)) / (2 * 1)
Separate the equations and simplify:
x = (6 + √20) / 2
x = (6 - √20) / 2
x = √5 + 3 or x = -√5 + 3
The values of a, b, and c that you would use to solve the equation using the Quadratic Formula are:
a = 1
b = -6
c = 4