# Solve Using the Square Root Property 0.10n^2-50n+1840=0 0.1n2-50n+1840=0
Factor the left side of the equation.
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 by 0.1 and simplify.
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
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.
(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 and solve.
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 and solve.
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     