Question

Joseph has started completing the square on the equation 3x2 - 7x + 12 = 0. He has worked to the point where he has the expression x2 - x = -4. Use complete sentences describe Joseph’s steps up to this point and whether or not his work is accurate.

Answer 1

x = 7/6 + (i sqrt(95))/6 or x = 7/6 - (i sqrt(95))/6 thus NO, x^2 - (7 x)/3 = -4 would be correct.

Explanation:

Solve for x:

3 x^2 - 7 x + 12 = 0

Hint: | Write the quadratic equation in standard form.

Divide both sides by 3:

x^2 - (7 x)/3 + 4 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 4 from both sides:

x^2 - (7 x)/3 = -4

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 49/36 to both sides:

x^2 - (7 x)/3 + 49/36 = -95/36

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 7/6)^2 = -95/36

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 7/6 = (i sqrt(95))/6 or x - 7/6 = -(i sqrt(95))/6

Hint: | Look at the first equation: Solve for x.

Add 7/6 to both sides:

x = 7/6 + (i sqrt(95))/6 or x - 7/6 = -(i sqrt(95))/6

Hint: | Look at the second equation: Solve for x.

Add 7/6 to both sides:

Answer: x = 7/6 + (i sqrt(95))/6 or x = 7/6 - (i sqrt(95))/6

Answer 2

Joseph's work wasn't accurate

Explanation:

Take a look at the image to understand the procedures