# Solve Using the Square Root Property x^2-5/2x-39/16=0 x2-52x-3916=0
Simplify each term.
Combine x and 52.
x2-x⋅52-3916=0
Move 5 to the left of x.
x2-5×2-3916=0
x2-5×2-3916=0
Multiply through by the least common denominator 16, then simplify.
Apply the distributive property.
16×2+16(-5×2)+16(-3916)=0
Simplify.
Cancel the common factor of 2.
Move the leading negative in -5×2 into the numerator.
16×2+16(-5×2)+16(-3916)=0
Factor 2 out of 16.
16×2+2(8)(-5×2)+16(-3916)=0
Cancel the common factor.
16×2+2⋅(8(-5×2))+16(-3916)=0
Rewrite the expression.
16×2+8(-5x)+16(-3916)=0
16×2+8(-5x)+16(-3916)=0
Multiply -5 by 8.
16×2-40x+16(-3916)=0
Cancel the common factor of 16.
Move the leading negative in -3916 into the numerator.
16×2-40x+16(-3916)=0
Cancel the common factor.
16×2-40x+16(-3916)=0
Rewrite the expression.
16×2-40x-39=0
16×2-40x-39=0
16×2-40x-39=0
16×2-40x-39=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=16, b=-40, and c=-39 into the quadratic formula and solve for x.
40±(-40)2-4⋅(16⋅-39)2⋅16
Simplify.
Simplify the numerator.
Raise -40 to the power of 2.
x=40±1600-4⋅(16⋅-39)2⋅16
Multiply 16 by -39.
x=40±1600-4⋅-6242⋅16
Multiply -4 by -624.
x=40±1600+24962⋅16
x=40±40962⋅16
Rewrite 4096 as 642.
x=40±6422⋅16
Pull terms out from under the radical, assuming positive real numbers.
x=40±642⋅16
x=40±642⋅16
Multiply 2 by 16.
x=40±6432
Simplify 40±6432.
x=5±84
x=5±84
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -40 to the power of 2.
x=40±1600-4⋅(16⋅-39)2⋅16
Multiply 16 by -39.
x=40±1600-4⋅-6242⋅16
Multiply -4 by -624.
x=40±1600+24962⋅16
x=40±40962⋅16
Rewrite 4096 as 642.
x=40±6422⋅16
Pull terms out from under the radical, assuming positive real numbers.
x=40±642⋅16
x=40±642⋅16
Multiply 2 by 16.
x=40±6432
Simplify 40±6432.
x=5±84
Change the ± to +.
x=5+84
x=134
x=134
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -40 to the power of 2.
x=40±1600-4⋅(16⋅-39)2⋅16
Multiply 16 by -39.
x=40±1600-4⋅-6242⋅16
Multiply -4 by -624.
x=40±1600+24962⋅16
x=40±40962⋅16
Rewrite 4096 as 642.
x=40±6422⋅16
Pull terms out from under the radical, assuming positive real numbers.
x=40±642⋅16
x=40±642⋅16
Multiply 2 by 16.
x=40±6432
Simplify 40±6432.
x=5±84
Change the ± to -.
x=5-84
Subtract 8 from 5.
x=-34
Move the negative in front of the fraction.
x=-34
x=-34
The final answer is the combination of both solutions.
x=134,-34
Solve Using the Square Root Property x^2-5/2x-39/16=0     