Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q.
3 + x - 3x2 = 9
A) (x -1/6)2 = 7/36
B) (x -1/3)2 =71/36
C) (x -1/6)2 = -71/36
D) (x -1/3)2 = -71/36
Please help me!
3 + x - 3x2 = 9
3 x^2 - x + 6 = 0
3 x^2 - x = -6
x^2 - 1/3 x = -2
x^2 - 1/3 x + (1/6)^2 = -2 + 1/36
( x - 1/6)^2 = -72/36 +1/36
@Damon It was C) like you said, thank you so much! Stay safe from the Coronavirus.
To transform the quadratic equation into the equation form (x + p)² = q using the method of completing the square, follow these steps:
1. Move the constant term to the other side of the equation:
3 + x - 3x² = 9
x - 3x² = 9 - 3
x - 3x² = 6
2. Divide the equation by the coefficient of the squared term (in this case, 3) to make the coefficient equal to 1:
(1/3)(x - 3x²) = (1/3)(6)
(x/3) - x² = 2
3. Rewrite the equation by adding and subtracting the square of half the coefficient of the linear term (in this case, x/6) inside the parentheses:
(x/3) - x² + (x/6)² = 2 + (x/6)²
4. Simplify the equation by squaring the term inside the parentheses:
(x/3) - x² + (x²/36) = 2 + (x²/36)
5. Combine the terms on the left side of the equation:
(x/3) + (x²/36) - x² = 2 + (x²/36)
6. Simplify further by combining like terms:
(x/3) - (35x²/36) = 2 + (x²/36)
7. Add the constant term on the right side of the equation to both sides:
(x/3) - (35x²/36) + (35/18) = 2 + (x²/36) + (35/18)
8. Simplify further by finding a common denominator and combining like terms:
[(12x - 35x²)/36] + (35/18) = [(36 + x²)/36]
9. Rewrite the equation in the desired form (x + p)² = q by completing the square:
[(12x - 35x²)/36] + (35/18) = [(6 + x/6)²]
10. Simplify both sides of the equation:
[(12x - 35x²)/36] + (35/18) = [(36 + x²)/36]
[(12x - 35x²)/36] + (70/36) = [(36 + x²)/36]
[(12x - 35x²) + 70] = 36 + x²
11. Rearrange the terms to isolate the squared term:
-35x² + 12x + 70 = x² + 36
12. Combine like terms:
-36x² + 12x + 70 = 36
13. Move all terms to one side to have the equation in the standard quadratic form:
-36x² + 12x + 34 = 0
Therefore, the correct answer choice would be D) (x -1/3)² = -71/36.