What are the solutions to the equation 192pi=2pi*x*16+2pi*x^2 ?

The solutions to the equation 192pi=2pi*x*16+2pi*x^2 are x=4(sqrt(10)-2),x=-4(2+sqrt(10))

Find the zeros of 192pi=2pi*x*16+2pi*x^2

The zeros of 192pi=2pi*x*16+2pi*x^2 are x=4(sqrt(10)-2),x=-4(2+sqrt(10))

192 π = 2 π \cdot x \cdot 16 + 2 π \cdot x^{2}

x = 4 (10 - 2), x = - 4 (2 + 10)

Decimal

x = 4.64911 \dots, x = - 20.64911 \dots

Solution steps

192 π = 2 π x \cdot 16 + 2 π x^{2}

Expand

2 π x \cdot 16 + 2 π x^{2} : 32 π x + 2 π x^{2}

192 π = 32 π x + 2 π x^{2}

Switch sides

32 π x + 2 π x^{2} = 192 π

Move

192 π

to the left side

32 π x + 2 π x^{2} - 192 π = 0

Write in the standard form

a x^{2} + b x + c = 0

2 π x^{2} + 32 π x - 192 π = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 32 π \pm ( 32 π ) ^{2} - 4 \cdot 2 π ( - 192 π )}{2 \cdot 2 π}

(32 π)^{2} - 4 \cdot 2 π (- 192 π) = 1610 π

x_{1, 2} = \frac{- 32 π \pm 16 10 π}{2 \cdot 2 π}

Separate the solutions

x_{1} = \frac{- 32 π + 16 10 π}{2 \cdot 2 π}, x_{2} = \frac{- 32 π - 16 10 π}{2 \cdot 2 π}

x = \frac{- 32 π + 16 10 π}{2 \cdot 2 π} : 4 (10 - 2)

x = \frac{- 32 π - 16 10 π}{2 \cdot 2 π} : - 4 (2 + 10)

The solutions to the quadratic equation are:

x = 4 (10 - 2), x = - 4 (2 + 10)

What are the solutions to the equation 192pi=2pi*x*16+2pi*x^2 ?
The solutions to the equation 192pi=2pi*x*16+2pi*x^2 are x=4(sqrt(10)-2),x=-4(2+sqrt(10))
Find the zeros of 192pi=2pi*x*16+2pi*x^2
The zeros of 192pi=2pi*x*16+2pi*x^2 are x=4(sqrt(10)-2),x=-4(2+sqrt(10))