# Solve for y -5y^2-3y-4y=-2 -5y2-3y-4y=-2
Subtract 4y from -3y.
-5y2-7y=-2
Move 2 to the left side of the equation by adding it to both sides.
-5y2-7y+2=0
Factor -1 out of -5y2-7y+2.
Factor -1 out of -5y2.
-(5y2)-7y+2=0
Factor -1 out of -7y.
-(5y2)-(7y)+2=0
Rewrite 2 as -1(-2).
-(5y2)-(7y)-1⋅-2=0
Factor -1 out of -(5y2)-(7y).
-(5y2+7y)-1⋅-2=0
Factor -1 out of -(5y2+7y)-1(-2).
-(5y2+7y-2)=0
-(5y2+7y-2)=0
Multiply each term in -(5y2+7y-2)=0 by -1
Multiply each term in -(5y2+7y-2)=0 by -1.
-(5y2+7y-2)⋅-1=0⋅-1
Simplify -(5y2+7y-2)⋅-1.
Apply the distributive property.
(-(5y2)-(7y)–2)⋅-1=0⋅-1
Simplify.
Multiply 5 by -1.
(-5y2-(7y)–2)⋅-1=0⋅-1
Multiply 7 by -1.
(-5y2-7y–2)⋅-1=0⋅-1
Multiply -1 by -2.
(-5y2-7y+2)⋅-1=0⋅-1
(-5y2-7y+2)⋅-1=0⋅-1
Apply the distributive property.
-5y2⋅-1-7y⋅-1+2⋅-1=0⋅-1
Simplify.
Multiply -1 by -5.
5y2-7y⋅-1+2⋅-1=0⋅-1
Multiply -1 by -7.
5y2+7y+2⋅-1=0⋅-1
Multiply 2 by -1.
5y2+7y-2=0⋅-1
5y2+7y-2=0⋅-1
5y2+7y-2=0⋅-1
Multiply 0 by -1.
5y2+7y-2=0
5y2+7y-2=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=5, b=7, and c=-2 into the quadratic formula and solve for y.
-7±72-4⋅(5⋅-2)2⋅5
Simplify.
Simplify the numerator.
Raise 7 to the power of 2.
y=-7±49-4⋅(5⋅-2)2⋅5
Multiply 5 by -2.
y=-7±49-4⋅-102⋅5
Multiply -4 by -10.
y=-7±49+402⋅5
Add 49 and 40.
y=-7±892⋅5
y=-7±892⋅5
Multiply 2 by 5.
y=-7±8910
y=-7±8910
The final answer is the combination of both solutions.
y=-7-8910,-7+8910
The result can be shown in multiple forms.
Exact Form:
y=-7-8910,-7+8910
Decimal Form:
y=0.24339811…,-1.64339811…
Solve for y -5y^2-3y-4y=-2

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