Answer:
-(9 y^2 - 20 y + 22) or if you need y = 10/9 + (7 i sqrt(2))/9 or y = 10/9 - (7 i sqrt(2))/9
Step-by-step explanation:
Simplify the following:
-(13 y^2 - 6 y + 20) + 4 y^2 + 12 y + 5 y - 3 y - 4 + 2
Grouping like terms, -(13 y^2 - 6 y + 20) + 4 y^2 + 12 y + 5 y - 3 y - 4 + 2 = -(13 y^2 - 6 y + 20) + 4 y^2 + (-3 y + 5 y + 12 y) + (2 - 4):
-(13 y^2 - 6 y + 20) + 4 y^2 + (-3 y + 5 y + 12 y) + (2 - 4)
-3 y + 5 y + 12 y = 14 y:
-(13 y^2 - 6 y + 20) + 4 y^2 + 14 y + (2 - 4)
2 - 4 = -2:
-(13 y^2 - 6 y + 20) + 4 y^2 + 14 y + -2
-(13 y^2 - 6 y + 20) = -13 y^2 + 6 y - 20:
-13 y^2 + 6 y - 20 + 4 y^2 + 14 y - 2
Grouping like terms, 4 y^2 - 13 y^2 + 14 y + 6 y - 20 - 2 = (-13 y^2 + 4 y^2) + (6 y + 14 y) + (-20 - 2):
(-13 y^2 + 4 y^2) + (6 y + 14 y) + (-20 - 2)
4 y^2 - 13 y^2 = -9 y^2:
-9 y^2 + (6 y + 14 y) + (-20 - 2)
6 y + 14 y = 20 y:
-9 y^2 + 20 y + (-20 - 2)
-20 - 2 = -22:
-9 y^2 + 20 y + -22
Factor -1 out of -9 y^2 + 20 y - 22:
Answer: -(9 y^2 - 20 y + 22)
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Solve for y:
-9 y^2 + 20 y - 22 = 0
Divide both sides by -9:
y^2 - (20 y)/9 + 22/9 = 0
Subtract 22/9 from both sides:
y^2 - (20 y)/9 = -22/9
Add 100/81 to both sides:
y^2 - (20 y)/9 + 100/81 = -98/81
Write the left hand side as a square:
(y - 10/9)^2 = -98/81
Take the square root of both sides:
y - 10/9 = (7 i sqrt(2))/9 or y - 10/9 = -(7 i sqrt(2))/9
Add 10/9 to both sides:
y = 10/9 + (7 i sqrt(2))/9 or y - 10/9 = -(7 i sqrt(2))/9
Add 10/9 to both sides:
Answer: y = 10/9 + (7 i sqrt(2))/9 or y = 10/9 - (7 i sqrt(2))/9
