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

Math
0=-x2+4.5x+5.5
Rewrite the equation as -x2+4.5x+5.5=0.
-x2+4.5x+5.5=0
Factor the left side of the equation.
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Factor -0.5 out of -x2+4.5x+5.5.
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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.
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Factor by grouping.
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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.
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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.
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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 by -0.5 and simplify.
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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
Factor by grouping.
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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.
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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.
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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 and solve.
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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 and solve.
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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.
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Divide each term in 2x=11 by 2.
2×2=112
Cancel the common factor of 2.
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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

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