# Evaluate (-(40) plus or minus square root of (40)^2-4*1*-400)/(2(1)) -(40)±(40)2-4⋅1⋅-4002(1)
Simplify the numerator.
Multiply -1 by 40.
-40±(40)2-4⋅1⋅-4002⋅1
Pull terms out from under the radical, assuming positive real numbers.
-40±40-4⋅1⋅-4002⋅1
Multiply -4 by 1.
-40±40-4⋅-4002⋅1
Multiply -4 by -400.
-40±40+16002⋅1
-40±40+16002⋅1
Simplify with factoring out.
Multiply 2 by 1.
-40±40+16002
Factor -1 out of -40±40.
-1(-(-40±40))+16002
Rewrite 1600 as -1(-1600).
-1(-(-40±40))-1(-1600)2
Factor -1 out of -1(-(-40±40))-1(-1600).
-1(-(-40±40)-1600)2
Move the negative in front of the fraction.
–(-40±40)-16002
–(-40±40)-16002
Use the positive value of the ± to find the first solution.
Cancel the common factor of -(-40+40)-1600 and 2.
Rewrite -1600 as -1(1600).
–(-40+40)-1(1600)2
Factor -1 out of -(-40+40)-1(1600).
–(-40+40+1600)2
Rewrite -(-40+40+1600) as -1(-40+40+1600).
–1(-40+40+1600)2
Factor 2 out of -1(-40+40+1600).
-2(-1(-20+20+800))2
Cancel the common factors.
Factor 2 out of 2.
-2(-1(-20+20+800))2(1)
Cancel the common factor.
-2(-1(-20+20+800))2⋅1
Rewrite the expression.
–1(-20+20+800)1
Divide -1(-20+20+800) by 1.
-(-1(-20+20+800))
-(-1(-20+20+800))
-(-1(-20+20+800))
Simplify the expression.
Rewrite -1(-20+20+800) as -(-20+20+800).
–(-20+20+800)
Add -20 and 20.
–(0+800)
Add 0 and 800.
-(-1⋅800)
Multiply -1 by 800.
–800
Multiply -1 by -800.
800
800
800
Use the negative value of the ± to find the second solution.
Cancel the common factor of -(-40-40)-1600 and 2.
Rewrite -1600 as -1(1600).
–(-40-40)-1(1600)2
Factor -1 out of -(-40-40)-1(1600).
–(-40-40+1600)2
Rewrite -(-40-40+1600) as -1(-40-40+1600).
–1(-40-40+1600)2
Factor 2 out of -1(-40-40+1600).
-2(-1(-20-20+800))2
Cancel the common factors.
Factor 2 out of 2.
-2(-1(-20-20+800))2(1)
Cancel the common factor.
-2(-1(-20-20+800))2⋅1
Rewrite the expression.
–1(-20-20+800)1
Divide -1(-20-20+800) by 1.
-(-1(-20-20+800))
-(-1(-20-20+800))
-(-1(-20-20+800))
Simplify the expression.
Rewrite -1(-20-20+800) as -(-20-20+800).
–(-20-20+800)
Subtract 20 from -20.
–(-40+800)
Add -40 and 800.
-(-1⋅760)
Multiply -1 by 760.
–760
Multiply -1 by -760.
760
760
760
The complete solution is the result of both the positive and negative portions of the solution.
800,760
Evaluate (-(40) plus or minus square root of (40)^2-4*1*-400)/(2(1))

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