Answer:
x = 6/7 + (2 i sqrt(19))/7 or x = 6/7 - (2 i sqrt(19))/7
Step-by-step explanation:
Solve for x:
7 x^2 - 12 x + 16 = 0
Hint: | Write the quadratic equation in standard form.
Divide both sides by 7:
x^2 - (12 x)/7 + 16/7 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 16/7 from both sides:
x^2 - (12 x)/7 = -16/7
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 36/49 to both sides:
x^2 - (12 x)/7 + 36/49 = -76/49
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 6/7)^2 = -76/49
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 6/7 = (2 i sqrt(19))/7 or x - 6/7 = -(2 i sqrt(19))/7
Hint: | Look at the first equation: Solve for x.
Add 6/7 to both sides:
x = 6/7 + (2 i sqrt(19))/7 or x - 6/7 = -(2 i sqrt(19))/7
Hint: | Look at the second equation: Solve for x.
Add 6/7 to both sides:
Answer: x = 6/7 + (2 i sqrt(19))/7 or x = 6/7 - (2 i sqrt(19))/7
