x2-52x-3916=0

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

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 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

Add 1600 and 2496.

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 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

Add 1600 and 2496.

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

Add 5 and 8.

x=134

x=134

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

Add 1600 and 2496.

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