4s-4s2=1

Move 1 to the left side of the equation by subtracting it from both sides.

4s-4s2-1=0

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.

-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