0.1n2-50n+1840=0

Factor 0.1 out of 0.1n2-50n+1840.

Factor 0.1 out of 0.1n2.

0.1(n2)-50n+1840=0

Factor 0.1 out of -50n.

0.1(n2)+0.1(-500n)+1840=0

Factor 0.1 out of 1840.

0.1n2+0.1(-500n)+0.1⋅18400=0

Factor 0.1 out of 0.1n2+0.1(-500n).

0.1(n2-500n)+0.1⋅18400=0

Factor 0.1 out of 0.1(n2-500n)+0.1⋅18400.

0.1(n2-500n+18400)=0

0.1(n2-500n+18400)=0

Factor.

Factor n2-500n+18400 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 18400 and whose sum is -500.

-460,-40

Write the factored form using these integers.

0.1((n-460)(n-40))=0

0.1((n-460)(n-40))=0

Remove unnecessary parentheses.

0.1(n-460)(n-40)=0

0.1(n-460)(n-40)=0

0.1(n-460)(n-40)=0

Divide each term in 0.1(n-460)(n-40)=0 by 0.1.

0.1(n-460)(n-40)0.1=00.1

Cancel the common factor of 0.1.

n2-500n+18400=00.1

Divide 0 by 0.1.

n2-500n+18400=0

n2-500n+18400=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 18400 and whose sum is -500.

-460,-40

Write the factored form using these integers.

(n-460)(n-40)=0

(n-460)(n-40)=0

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

n-460=0

n-40=0

Set the first factor equal to 0.

n-460=0

Add 460 to both sides of the equation.

n=460

n=460

Set the next factor equal to 0.

n-40=0

Add 40 to both sides of the equation.

n=40

n=40

The final solution is all the values that make (n-460)(n-40)=0 true.

n=460,40

Solve Using the Square Root Property 0.10n^2-50n+1840=0