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

Math
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.
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Simplify the numerator.
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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.
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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 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⋅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.
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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 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⋅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.
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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

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