# Solve for s 4s-4s^2=1 4s-4s2=1
Move 1 to the left side of the equation by subtracting it from both sides.
4s-4s2-1=0
Factor the left side of the equation.
Let u=s. Substitute u for all occurrences of s.
4u-4u2-1
Factor by grouping.
Reorder terms.
-4u2+4u-1
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-4⋅-1=4 and whose sum is b=4.
Factor 4 out of 4u.
-4u2+4(u)-1
Rewrite 4 as 2 plus 2
-4u2+(2+2)u-1
Apply the distributive property.
-4u2+2u+2u-1
-4u2+2u+2u-1
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(-4u2+2u)+2u-1
Factor out the greatest common factor (GCF) from each group.
2u(-2u+1)-(-2u+1)
2u(-2u+1)-(-2u+1)
Factor the polynomial by factoring out the greatest common factor, -2u+1.
(-2u+1)(2u-1)
(-2u+1)(2u-1)
Replace all occurrences of u with s.
(-2s+1)(2s-1)
Replace the left side with the factored expression.
(-2s+1)(2s-1)=0
(-2s+1)(2s-1)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
-2s+1=0
2s-1=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
-2s+1=0
Subtract 1 from both sides of the equation.
-2s=-1
Divide each term by -2 and simplify.
Divide each term in -2s=-1 by -2.
-2s-2=-1-2
Cancel the common factor of -2.
Cancel the common factor.
-2s-2=-1-2
Divide s by 1.
s=-1-2
s=-1-2
Dividing two negative values results in a positive value.
s=12
s=12
s=12
The final solution is all the values that make (-2s+1)(2s-1)=0 true.
s=12
The result can be shown in multiple forms.
Exact Form:
s=12
Decimal Form:
s=0.5
Solve for s 4s-4s^2=1

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