solve the equation by completing the square
3x^2-12x+1=0
x^2-4x+1/3=0
x^2-4x = -1/3
x^2-4x+4=4-1/3
(x-2)^2=(sqrt (3 2/3))^2
x-2=+- sqrt (3 2/3)
or...
3x^2 -12x+ 36 = 35
(x-6)^2 = 35
x-6 = square root of 35
x= 6+ or 6- the square root of 35
To solve the equation by completing the square, follow these steps:
1. Make sure the coefficient of the x^2 term is 1. In this case, the coefficient is already 3, so no need to change anything.
Equation: 3x^2 - 12x + 1 = 0
2. Move the constant term to the other side of the equation:
3x^2 - 12x = -1
3. Divide the coefficient of the x term by 2 and square it. Add this result to both sides of the equation:
Take half of -12 and square it: (-12 / 2)^2 = (-6)^2 = 36
3x^2 - 12x + 36 = -1 + 36
4. Simplify both sides of the equation:
3x^2 - 12x + 36 = 35
5. Rewrite the left side of the equation as a perfect square trinomial. To do this, factor the square of the binomial obtained in step 3:
(x - 6)^2 = 35
6. Take the square root of both sides and remember to consider both the positive and negative square roots:
x - 6 = ±√35
7. Solve for x by adding 6 to both sides:
x = 6 ± √35
Therefore, the solutions to the equation 3x^2 - 12x + 1 = 0, by completing the square, are x = 6 ± √35.