To solve: 3y2−y−14=0

Roger Smith

Roger Smith

Answered

2021-12-28

To solve: 3y2y14=0

Answer & Explanation

David Clayton

David Clayton

Expert

2021-12-29Added 36 answers

Step 1
Determine the quadratic equations
chumants6g

chumants6g

Expert

2021-12-30Added 33 answers

Step 1
Given: 3y2y14=0
All equations of the form ax2+bx+c=0 can be solved using the quadratic formula: b±b24ac2a. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
This equation is in standard form: ax2+bx+c=0. Substitute 3 for a, -1 for b, and -14 for c in the quadratic formula, b±b24ac2a
y=(1)±14×3(14)2×3
Multiply -4 times 3.
y=(1)±112(14)2×3
Multiply -12 times -14.
y=(1)±1+1682×3
Add 1 to 168.
y=(1)±1692×3
Take the square root of 169.
y=(1)±132×3
The opposite of -1 is 1.
y=1±132×3
Multiply 2 times 3.
y=1±136
Now solve the equation y=1±136 when ± is plus. Add 1 to 13.
y=146
Reduce the fraction 146 to lowest terms by extracting and canceling out 2
y=73
Now solve the equation y=1±136 when ± is minus. Subtract 13 from 1.
y=126
Divide -12 by 6
y=2
The equation is now solved
y=73
y=2

karton

karton

Expert

2022-01-09Added 439 answers

Step 1
Split the middle term -y as 6y and -7y
Replace -y with +6y-7y in 3y2y14=0
3y27y+6y14=0
The above equation can be written as 3y×y7×y+2×3y2×7
Apply distribtive property for first two terms and last two terms,
3y×y7×y+2×3y2×7=y(3y7)+2(3y7)
Again apply distributive property for y(3y-7)+2(3y-7)
y(3y-7)+2(3y-7)=(3y-7)(y+2)
So the factors are (3y-7) and (y+2)
3y2y14=(3y7)(y+2)
To find the value of y,
Take 3y-7=0
Add 7 on both sides,
3y-7+7=0+7
3y=7
Divide by 3 on both sides,
3y3=73
y=73
Take y+2=0
Subtract 2 on both sides,
y-2+2=0-2
y=-2
The factors are y=73 and y=-2
So, the values of y are 73 and -2

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