Very confused, it says to simplify answer & express complex numbers in terms of i.
-
This is a quadratic equation, so you want to use the Quadratic Formula.
3x^2 - 7x = -6
3x^2 - 7x + 6 = 0
a = 3, b = -7, c = 6
x = 7/6 ± i √23/6
3x^2 - 7x = -6
3x^2 - 7x + 6 = 0
a = 3, b = -7, c = 6
x = 7/6 ± i √23/6
-
3x² - 7x = -6
Divide both sides by 3:
x² - (7/3)x = -2
Add to both sides to complete the square:
(x² - (7/3)x + (7/6)²) = -2 + (7/6)²
Condense the square:
(x - 7/6)² = [-72 + 49]/36
Take the square root:
x - 7/6 = ± i√(23)/6
Add 7/6 to both sides:
x = 7/6 ± i*√(23)/6
==============================
The question says use the quadratic formula, so:
ax² + bx + c = 0
3x² - 7x + 6 = 0
x = [-b ± √(b² - 4ac)] / (2a)
x = [7 ± i√(23)] / 6
And you get the same answer either way.
Divide both sides by 3:
x² - (7/3)x = -2
Add to both sides to complete the square:
(x² - (7/3)x + (7/6)²) = -2 + (7/6)²
Condense the square:
(x - 7/6)² = [-72 + 49]/36
Take the square root:
x - 7/6 = ± i√(23)/6
Add 7/6 to both sides:
x = 7/6 ± i*√(23)/6
==============================
The question says use the quadratic formula, so:
ax² + bx + c = 0
3x² - 7x + 6 = 0
x = [-b ± √(b² - 4ac)] / (2a)
x = [7 ± i√(23)] / 6
And you get the same answer either way.
-
3x^2 - 7x = -6
3x^2 - 7x + 6 = 0
-36/23(x - 7/6)^2 = 1
3(x - 7/6)^2 + 23/12 = 0
Complex solutions:
x = 1/6(7 - i√23)
x = 1/6(7 + i√23)
3x^2 - 7x + 6 = 0
-36/23(x - 7/6)^2 = 1
3(x - 7/6)^2 + 23/12 = 0
Complex solutions:
x = 1/6(7 - i√23)
x = 1/6(7 + i√23)
-
3x^2 - 7x = -6
3x^2 - 7x + 6 = 0
(7 ± √-23) / 6
x = (7 ± i√23) / 6
3x^2 - 7x + 6 = 0
(7 ± √-23) / 6
x = (7 ± i√23) / 6