16×2-16x+41=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=16, b=-16, and c=41 into the quadratic formula and solve for x.

16±(-16)2-4⋅(16⋅41)2⋅16

Simplify the numerator.

Raise -16 to the power of 2.

x=16±256-4⋅(16⋅41)2⋅16

Multiply 16 by 41.

x=16±256-4⋅6562⋅16

Multiply -4 by 656.

x=16±256-26242⋅16

Subtract 2624 from 256.

x=16±-23682⋅16

Rewrite -2368 as -1(2368).

x=16±-1⋅23682⋅16

Rewrite -1(2368) as -1⋅2368.

x=16±-1⋅23682⋅16

Rewrite -1 as i.

x=16±i⋅23682⋅16

Rewrite 2368 as 82⋅37.

Factor 64 out of 2368.

x=16±i⋅64(37)2⋅16

Rewrite 64 as 82.

x=16±i⋅82⋅372⋅16

x=16±i⋅82⋅372⋅16

Pull terms out from under the radical.

x=16±i⋅(837)2⋅16

Move 8 to the left of i.

x=16±8i372⋅16

x=16±8i372⋅16

Multiply 2 by 16.

x=16±8i3732

Simplify 16±8i3732.

x=2±i374

x=2±i374

Simplify the numerator.

Raise -16 to the power of 2.

x=16±256-4⋅(16⋅41)2⋅16

Multiply 16 by 41.

x=16±256-4⋅6562⋅16

Multiply -4 by 656.

x=16±256-26242⋅16

Subtract 2624 from 256.

x=16±-23682⋅16

Rewrite -2368 as -1(2368).

x=16±-1⋅23682⋅16

Rewrite -1(2368) as -1⋅2368.

x=16±-1⋅23682⋅16

Rewrite -1 as i.

x=16±i⋅23682⋅16

Rewrite 2368 as 82⋅37.

Factor 64 out of 2368.

x=16±i⋅64(37)2⋅16

Rewrite 64 as 82.

x=16±i⋅82⋅372⋅16

x=16±i⋅82⋅372⋅16

Pull terms out from under the radical.

x=16±i⋅(837)2⋅16

Move 8 to the left of i.

x=16±8i372⋅16

x=16±8i372⋅16

Multiply 2 by 16.

x=16±8i3732

Simplify 16±8i3732.

x=2±i374

Change the ± to +.

x=2+i374

x=2+i374

Simplify the numerator.

Raise -16 to the power of 2.

x=16±256-4⋅(16⋅41)2⋅16

Multiply 16 by 41.

x=16±256-4⋅6562⋅16

Multiply -4 by 656.

x=16±256-26242⋅16

Subtract 2624 from 256.

x=16±-23682⋅16

Rewrite -2368 as -1(2368).

x=16±-1⋅23682⋅16

Rewrite -1(2368) as -1⋅2368.

x=16±-1⋅23682⋅16

Rewrite -1 as i.

x=16±i⋅23682⋅16

Rewrite 2368 as 82⋅37.

Factor 64 out of 2368.

x=16±i⋅64(37)2⋅16

Rewrite 64 as 82.

x=16±i⋅82⋅372⋅16

x=16±i⋅82⋅372⋅16

Pull terms out from under the radical.

x=16±i⋅(837)2⋅16

Move 8 to the left of i.

x=16±8i372⋅16

x=16±8i372⋅16

Multiply 2 by 16.

x=16±8i3732

Simplify 16±8i3732.

x=2±i374

Change the ± to -.

x=2-i374

x=2-i374

The final answer is the combination of both solutions.

x=2+i374,2-i374

Solve using the Square Root Property 16x^2-16x+41=0