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

Math
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.
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Simplify the numerator.
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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.
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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 expression to solve for the + portion of the ±.
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Simplify the numerator.
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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.
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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 expression to solve for the – portion of the ±.
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Simplify the numerator.
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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.
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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

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