0=-x2+4.5x+5.5

Rewrite the equation as -x2+4.5x+5.5=0.

-x2+4.5x+5.5=0

Factor -0.5 out of -x2+4.5x+5.5.

Factor -0.5 out of -x2.

-0.5(2×2)+4.5x+5.5=0

Factor -0.5 out of 4.5x.

-0.5(2×2)-0.5(-9x)+5.5=0

Factor -0.5 out of 5.5.

-0.5(2×2)-0.5(-9x)-0.5⋅-11=0

Factor -0.5 out of -0.5(2×2)-0.5(-9x).

-0.5(2×2-9x)-0.5⋅-11=0

Factor -0.5 out of -0.5(2×2-9x)-0.5(-11).

-0.5(2×2-9x-11)=0

-0.5(2×2-9x-11)=0

Factor.

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-11=-22 and whose sum is b=-9.

Factor -9 out of -9x.

-0.5(2×2-9x-11)=0

Rewrite -9 as 2 plus -11

-0.5(2×2+(2-11)x-11)=0

Apply the distributive property.

-0.5(2×2+2x-11x-11)=0

-0.5(2×2+2x-11x-11)=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

-0.5((2×2+2x)-11x-11)=0

Factor out the greatest common factor (GCF) from each group.

-0.5(2x(x+1)-11(x+1))=0

-0.5(2x(x+1)-11(x+1))=0

Factor the polynomial by factoring out the greatest common factor, x+1.

-0.5((x+1)(2x-11))=0

-0.5((x+1)(2x-11))=0

Remove unnecessary parentheses.

-0.5(x+1)(2x-11)=0

-0.5(x+1)(2x-11)=0

-0.5(x+1)(2x-11)=0

Divide each term in -0.5(x+1)(2x-11)=0 by -0.5.

-0.5(x+1)(2x-11)-0.5=0-0.5

Cancel the common factor of -0.5.

2×2-9x-11=0-0.5

Divide 0 by -0.5.

2×2-9x-11=0

2×2-9x-11=0

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-11=-22 and whose sum is b=-9.

Factor -9 out of -9x.

2×2-9x-11=0

Rewrite -9 as 2 plus -11

2×2+(2-11)x-11=0

Apply the distributive property.

2×2+2x-11x-11=0

2×2+2x-11x-11=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2×2+2x)-11x-11=0

Factor out the greatest common factor (GCF) from each group.

2x(x+1)-11(x+1)=0

2x(x+1)-11(x+1)=0

Factor the polynomial by factoring out the greatest common factor, x+1.

(x+1)(2x-11)=0

(x+1)(2x-11)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x+1=0

2x-11=0

Set the first factor equal to 0.

x+1=0

Subtract 1 from both sides of the equation.

x=-1

x=-1

Set the next factor equal to 0.

2x-11=0

Add 11 to both sides of the equation.

2x=11

Divide each term by 2 and simplify.

Divide each term in 2x=11 by 2.

2×2=112

Cancel the common factor of 2.

Cancel the common factor.

2×2=112

Divide x by 1.

x=112

x=112

x=112

x=112

The final solution is all the values that make (x+1)(2x-11)=0 true.

x=-1,112

Solve using the Square Root Property 0=-x^2+4.5x+5.5