3y² + 5y - 8 = 0 That is supposed to read 3y squared.
I must solve the equation(i.e. x=4 0r 6).
3y² + 5y - 8 = 0
Multiply the red 3 by the green 8. Get 24.
Think of two numbers such that when you
(1) MULTIPLY them, you get 24
(2) SUBTRACT them, you get the blue 5.
Note: [For other problems, if the sign before the green 8 had been +
instead of -, step (2) would have been "ADD" instead of "SUBTRACT".)
These numbers are 8 and 3, because when you
multiply 8 by 3, you get 24 and when you
subtract 8 - 3, you get 5.
Replace the blue 5 by (8 - 3)
3y² + 5y - 8 = 0
3y² + (8 - 3)y - 8 = 0
Remove the parentheses by using the
distributive principle:
3y² + 8y - 3y - 8 = 0
Factor y out of the first two terms:
y(3y + 8) - 3y - 8 = 0
Factor -1 out of the last two terms:
y(3y + 8) - 1(3y + 8) = 0
For clarity I will color the two parentheses purple
y(3y + 8) - 1(3y + 8) = 0
Notice that the two purple factors are the same:
Take out the purple factor and leave the black factors in
another parentheses:
(3y + 8)(y - 1) = 0
(3y + 8)(y - 1) = 0
Set the expression within the first parentheses equal to zero:
3y + 8 = 0
3y = -8
y = -8/3
Set the expression within the second parentheses equal to zero:
y - 1 = 0
y = 1
So there are two solutions: y = -8/3 and y = 1
Edwin
