Solve using the Square Root Property -2y=5y^2-7

Math
-2y=5y2-7
Subtract 5y2 from both sides of the equation.
-2y-5y2=-7
Move 7 to the left side of the equation by adding it to both sides.
-2y-5y2+7=0
Factor the left side of the equation.
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Let u=y. Substitute u for all occurrences of y.
-2u-5u2+7
Factor by grouping.
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Reorder terms.
-5u2-2u+7
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-5⋅7=-35 and whose sum is b=-2.
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Factor -2 out of -2u.
-5u2-2(u)+7
Rewrite -2 as 5 plus -7
-5u2+(5-7)u+7
Apply the distributive property.
-5u2+5u-7u+7
-5u2+5u-7u+7
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(-5u2+5u)-7u+7
Factor out the greatest common factor (GCF) from each group.
5u(-u+1)+7(-u+1)
5u(-u+1)+7(-u+1)
Factor the polynomial by factoring out the greatest common factor, -u+1.
(-u+1)(5u+7)
(-u+1)(5u+7)
Replace all occurrences of u with y.
(-y+1)(5y+7)
Replace the left side with the factored expression.
(-y+1)(5y+7)=0
(-y+1)(5y+7)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
-y+1=0
5y+7=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
-y+1=0
Subtract 1 from both sides of the equation.
-y=-1
Multiply each term in -y=-1 by -1
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Multiply each term in -y=-1 by -1.
(-y)⋅-1=(-1)⋅-1
Multiply (-y)⋅-1.
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Multiply -1 by -1.
1y=(-1)⋅-1
Multiply y by 1.
y=(-1)⋅-1
y=(-1)⋅-1
Multiply -1 by -1.
y=1
y=1
y=1
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
5y+7=0
Subtract 7 from both sides of the equation.
5y=-7
Divide each term by 5 and simplify.
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Divide each term in 5y=-7 by 5.
5y5=-75
Cancel the common factor of 5.
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Cancel the common factor.
5y5=-75
Divide y by 1.
y=-75
y=-75
Move the negative in front of the fraction.
y=-75
y=-75
y=-75
The final solution is all the values that make (-y+1)(5y+7)=0 true.
y=1,-75
Solve using the Square Root Property -2y=5y^2-7

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