Solve by completing the square:
x^2-6x+3=0
show steps please
To solve the quadratic equation by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation.
Given equation: x^2 - 6x + 3 = 0
Subtracting 3 from both sides:
x^2 - 6x = -3
Step 2: Make the coefficient of the x^2 term equal to 1.
In this case, the coefficient is already 1.
Step 3: Take half of the coefficient of the x term and square it. Add this value to both sides of the equation.
The coefficient of the x term is -6:
(-6/2)^2 = 9
Adding 9 to both sides of the equation:
x^2 - 6x + 9 = -3 + 9
x^2 - 6x + 9 = 6
Step 4: Rewrite the left side of the equation as a perfect square trinomial.
The left side can be written as (x - a)^2, where 'a' is equal to half the coefficient of the x term.
In this case, 'a' is -3.
Rewriting the equation:
(x - 3)^2 = 6
Step 5: Take the square root of both sides of the equation.
Taking the square root of both sides:
√((x - 3)^2) = √(6)
This simplifies to:
x - 3 = ±√(6)
Step 6: Solve for x.
Adding 3 to both sides:
x = 3 ±√(6)
Therefore, the solutions to the quadratic equation x^2 - 6x + 3 = 0 are:
x = 3 + √(6) and x = 3 - √(6).