16×2-16x+63=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=16, b=-16, and c=63 into the quadratic formula and solve for x.

16±(-16)2-4⋅(16⋅63)2⋅16

Simplify the numerator.

Raise -16 to the power of 2.

x=16±256-4⋅(16⋅63)2⋅16

Multiply 16 by 63.

x=16±256-4⋅10082⋅16

Multiply -4 by 1008.

x=16±256-40322⋅16

Subtract 4032 from 256.

x=16±-37762⋅16

Rewrite -3776 as -1(3776).

x=16±-1⋅37762⋅16

Rewrite -1(3776) as -1⋅3776.

x=16±-1⋅37762⋅16

Rewrite -1 as i.

x=16±i⋅37762⋅16

Rewrite 3776 as 82⋅59.

Factor 64 out of 3776.

x=16±i⋅64(59)2⋅16

Rewrite 64 as 82.

x=16±i⋅82⋅592⋅16

x=16±i⋅82⋅592⋅16

Pull terms out from under the radical.

x=16±i⋅(859)2⋅16

Move 8 to the left of i.

x=16±8i592⋅16

x=16±8i592⋅16

Multiply 2 by 16.

x=16±8i5932

Simplify 16±8i5932.

x=2±i594

x=2±i594

Simplify the numerator.

Raise -16 to the power of 2.

x=16±256-4⋅(16⋅63)2⋅16

Multiply 16 by 63.

x=16±256-4⋅10082⋅16

Multiply -4 by 1008.

x=16±256-40322⋅16

Subtract 4032 from 256.

x=16±-37762⋅16

Rewrite -3776 as -1(3776).

x=16±-1⋅37762⋅16

Rewrite -1(3776) as -1⋅3776.

x=16±-1⋅37762⋅16

Rewrite -1 as i.

x=16±i⋅37762⋅16

Rewrite 3776 as 82⋅59.

Factor 64 out of 3776.

x=16±i⋅64(59)2⋅16

Rewrite 64 as 82.

x=16±i⋅82⋅592⋅16

x=16±i⋅82⋅592⋅16

Pull terms out from under the radical.

x=16±i⋅(859)2⋅16

Move 8 to the left of i.

x=16±8i592⋅16

x=16±8i592⋅16

Multiply 2 by 16.

x=16±8i5932

Simplify 16±8i5932.

x=2±i594

Change the ± to +.

x=2+i594

x=2+i594

Simplify the numerator.

Raise -16 to the power of 2.

x=16±256-4⋅(16⋅63)2⋅16

Multiply 16 by 63.

x=16±256-4⋅10082⋅16

Multiply -4 by 1008.

x=16±256-40322⋅16

Subtract 4032 from 256.

x=16±-37762⋅16

Rewrite -3776 as -1(3776).

x=16±-1⋅37762⋅16

Rewrite -1(3776) as -1⋅3776.

x=16±-1⋅37762⋅16

Rewrite -1 as i.

x=16±i⋅37762⋅16

Rewrite 3776 as 82⋅59.

Factor 64 out of 3776.

x=16±i⋅64(59)2⋅16

Rewrite 64 as 82.

x=16±i⋅82⋅592⋅16

x=16±i⋅82⋅592⋅16

Pull terms out from under the radical.

x=16±i⋅(859)2⋅16

Move 8 to the left of i.

x=16±8i592⋅16

x=16±8i592⋅16

Multiply 2 by 16.

x=16±8i5932

Simplify 16±8i5932.

x=2±i594

Change the ± to -.

x=2-i594

x=2-i594

The final answer is the combination of both solutions.

x=2+i594,2-i594

Solve Using the Square Root Property 16x^2-16x+63=0