Solve by completing the square 3x(sqaured) - 8x - 6 = 0.
Is it 4 - the square root of 34 / 3 and 4 + the square root of 34 / 3?
3x^2 - 8x - 6 = 0
x^2 - 8/3 x = 2
x^2 - 8/3 x + (4/3)^2 = 2 + (4/3)^2
(x - 4/3)^2 = 2 + 16/9 = 34/9
x - 4/3 = ±√34/3
x = 4/3 ±√34/3
x = (4±√34)/3
you are correct
Thank you!
To solve the quadratic equation 3x^2 - 8x - 6 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
3x^2 - 8x = 6
Step 2: Divide the entire equation by the coefficient of x^2 to make the coefficient 1:
x^2 - (8/3)x = 2
Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 - (8/3)x + (8/6)^2 = 2 + (8/6)^2
x^2 - (8/3)x + 64/36 = 2 + 64/36
Simplifying the equation gives:
x^2 - (8/3)x + 64/36 = 72/36 + 64/36
x^2 - (8/3)x + 64/36 = 136/36
Step 4: Rewrite the left side of the equation as a perfect square trinomial:
(x - (4/3))^2 = 136/36
Step 5: Take the square root of both sides of the equation:
√((x - (4/3))^2) = ±√(136/36)
Step 6: Solve for x by isolating it on one side:
x - (4/3) = ±√(136/36)
Step 7: Add (4/3) to both sides:
x = (4/3) ±√(136/36)
Simplifying the square root:
x = (4/3) ±√(34/9)
Step 8: Simplify the expression:
x = (4 ± √34)/3
So the solutions to the quadratic equation 3x^2 - 8x - 6 = 0, after completing the square, are:
x = (4 + √34)/3 and x = (4 - √34)/3
Therefore, the answer is:
x = (4 + √34)/3 and x = (4 - √34)/3