x2-32x-2716=0

Combine x and 32.

x2-x⋅32-2716=0

Move 3 to the left of x.

x2-3×2-2716=0

x2-3×2-2716=0

Apply the distributive property.

16×2+16(-3×2)+16(-2716)=0

Simplify.

Cancel the common factor of 2.

Move the leading negative in -3×2 into the numerator.

16×2+16(-3×2)+16(-2716)=0

Factor 2 out of 16.

16×2+2(8)(-3×2)+16(-2716)=0

Cancel the common factor.

16×2+2⋅(8(-3×2))+16(-2716)=0

Rewrite the expression.

16×2+8(-3x)+16(-2716)=0

16×2+8(-3x)+16(-2716)=0

Multiply -3 by 8.

16×2-24x+16(-2716)=0

Cancel the common factor of 16.

Move the leading negative in -2716 into the numerator.

16×2-24x+16(-2716)=0

Cancel the common factor.

16×2-24x+16(-2716)=0

Rewrite the expression.

16×2-24x-27=0

16×2-24x-27=0

16×2-24x-27=0

16×2-24x-27=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=16, b=-24, and c=-27 into the quadratic formula and solve for x.

24±(-24)2-4⋅(16⋅-27)2⋅16

Simplify the numerator.

Raise -24 to the power of 2.

x=24±576-4⋅(16⋅-27)2⋅16

Multiply 16 by -27.

x=24±576-4⋅-4322⋅16

Multiply -4 by -432.

x=24±576+17282⋅16

Add 576 and 1728.

x=24±23042⋅16

Rewrite 2304 as 482.

x=24±4822⋅16

Pull terms out from under the radical, assuming positive real numbers.

x=24±482⋅16

x=24±482⋅16

Multiply 2 by 16.

x=24±4832

Simplify 24±4832.

x=3±64

x=3±64

Simplify the numerator.

Raise -24 to the power of 2.

x=24±576-4⋅(16⋅-27)2⋅16

Multiply 16 by -27.

x=24±576-4⋅-4322⋅16

Multiply -4 by -432.

x=24±576+17282⋅16

Add 576 and 1728.

x=24±23042⋅16

Rewrite 2304 as 482.

x=24±4822⋅16

Pull terms out from under the radical, assuming positive real numbers.

x=24±482⋅16

x=24±482⋅16

Multiply 2 by 16.

x=24±4832

Simplify 24±4832.

x=3±64

Change the ± to +.

x=3+64

Add 3 and 6.

x=94

x=94

Simplify the numerator.

Raise -24 to the power of 2.

x=24±576-4⋅(16⋅-27)2⋅16

Multiply 16 by -27.

x=24±576-4⋅-4322⋅16

Multiply -4 by -432.

x=24±576+17282⋅16

Add 576 and 1728.

x=24±23042⋅16

Rewrite 2304 as 482.

x=24±4822⋅16

Pull terms out from under the radical, assuming positive real numbers.

x=24±482⋅16

x=24±482⋅16

Multiply 2 by 16.

x=24±4832

Simplify 24±4832.

x=3±64

Change the ± to -.

x=3-64

Subtract 6 from 3.

x=-34

Move the negative in front of the fraction.

x=-34

x=-34

The final answer is the combination of both solutions.

x=94,-34

Solve Using the Square Root Property x^2-3/2x-27/16=0