Solve using the Square Root Property 16x^2-16x+47=0

Math
16×2-16x+47=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=16, b=-16, and c=47 into the quadratic formula and solve for x.
16±(-16)2-4⋅(16⋅47)2⋅16
Simplify.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Raise -16 to the power of 2.
x=16±256-4⋅(16⋅47)2⋅16
Multiply 16 by 47.
x=16±256-4⋅7522⋅16
Multiply -4 by 752.
x=16±256-30082⋅16
Subtract 3008 from 256.
x=16±-27522⋅16
Rewrite -2752 as -1(2752).
x=16±-1⋅27522⋅16
Rewrite -1(2752) as -1⋅2752.
x=16±-1⋅27522⋅16
Rewrite -1 as i.
x=16±i⋅27522⋅16
Rewrite 2752 as 82⋅43.
Tap for more steps…
Factor 64 out of 2752.
x=16±i⋅64(43)2⋅16
Rewrite 64 as 82.
x=16±i⋅82⋅432⋅16
x=16±i⋅82⋅432⋅16
Pull terms out from under the radical.
x=16±i⋅(843)2⋅16
Move 8 to the left of i.
x=16±8i432⋅16
x=16±8i432⋅16
Multiply 2 by 16.
x=16±8i4332
Simplify 16±8i4332.
x=2±i434
x=2±i434
Simplify the expression to solve for the + portion of the ±.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Raise -16 to the power of 2.
x=16±256-4⋅(16⋅47)2⋅16
Multiply 16 by 47.
x=16±256-4⋅7522⋅16
Multiply -4 by 752.
x=16±256-30082⋅16
Subtract 3008 from 256.
x=16±-27522⋅16
Rewrite -2752 as -1(2752).
x=16±-1⋅27522⋅16
Rewrite -1(2752) as -1⋅2752.
x=16±-1⋅27522⋅16
Rewrite -1 as i.
x=16±i⋅27522⋅16
Rewrite 2752 as 82⋅43.
Tap for more steps…
Factor 64 out of 2752.
x=16±i⋅64(43)2⋅16
Rewrite 64 as 82.
x=16±i⋅82⋅432⋅16
x=16±i⋅82⋅432⋅16
Pull terms out from under the radical.
x=16±i⋅(843)2⋅16
Move 8 to the left of i.
x=16±8i432⋅16
x=16±8i432⋅16
Multiply 2 by 16.
x=16±8i4332
Simplify 16±8i4332.
x=2±i434
Change the ± to +.
x=2+i434
x=2+i434
Simplify the expression to solve for the – portion of the ±.
Tap for more steps…
Simplify the numerator.
Tap for more steps…
Raise -16 to the power of 2.
x=16±256-4⋅(16⋅47)2⋅16
Multiply 16 by 47.
x=16±256-4⋅7522⋅16
Multiply -4 by 752.
x=16±256-30082⋅16
Subtract 3008 from 256.
x=16±-27522⋅16
Rewrite -2752 as -1(2752).
x=16±-1⋅27522⋅16
Rewrite -1(2752) as -1⋅2752.
x=16±-1⋅27522⋅16
Rewrite -1 as i.
x=16±i⋅27522⋅16
Rewrite 2752 as 82⋅43.
Tap for more steps…
Factor 64 out of 2752.
x=16±i⋅64(43)2⋅16
Rewrite 64 as 82.
x=16±i⋅82⋅432⋅16
x=16±i⋅82⋅432⋅16
Pull terms out from under the radical.
x=16±i⋅(843)2⋅16
Move 8 to the left of i.
x=16±8i432⋅16
x=16±8i432⋅16
Multiply 2 by 16.
x=16±8i4332
Simplify 16±8i4332.
x=2±i434
Change the ± to -.
x=2-i434
x=2-i434
The final answer is the combination of both solutions.
x=2+i434,2-i434
Solve using the Square Root Property 16x^2-16x+47=0

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top