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Popular >

(((y^2+4y+68))/(16-4))^2+(y+2)^2=36

Solution

(\frac{( y ^{2} + 4 y + 68 )}{16 - 4})^{2} + (y + 2)^{2} = 36

Solution

y \approx - 0.01434 \dots, y \approx - 3.98565 \dots

Solution steps

(\frac{( y ^{2} + 4 y + 68 )}{16 - 4})^{2} + (y + 2)^{2} = 36

Expand

(\frac{y ^{2} + 4 y + 68}{16 - 4})^{2} + (y + 2)^{2} : \frac{y ^{4}}{144} + \frac{y ^{3}}{18} + \frac{37 y ^{2}}{18} + \frac{70 y}{9} + \frac{325}{9}

\frac{y ^{4}}{144} + \frac{y ^{3}}{18} + \frac{37 y ^{2}}{18} + \frac{70 y}{9} + \frac{325}{9} = 36

Move

36

to the left side

\frac{y ^{4}}{144} + \frac{y ^{3} + 37 y ^{2}}{18} + \frac{70 y + 325}{9} - 36 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

\frac{1 \cdot y ^{4}}{144} + \frac{1 \cdot y ^{3}}{18} + \frac{37 y ^{2}}{18} + \frac{70 y}{9} + \frac{325}{9} - 36 = 0

Find one solution for

0.00694 \dots y^{4} + 0.05555 \dots y^{3} + 2.05555 \dots y^{2} + 7.77777 \dots y + 0.11111 \dots = 0

using Newton-Raphson:

y \approx - 0.01434 \dots

Apply long division:

\frac{\frac{1 \cdot y ^{4}}{144} + \frac{1 \cdot y ^{3}}{18} + \frac{37 y ^{2}}{18} + \frac{70 y}{9} + \frac{325}{9} - 36}{y + 0.01434 \dots} = 0.00694 \dots y^{3} + 0.05545 \dots y^{2} + 2.05476 \dots y + 7.74831 \dots

0.00694 \dots y^{3} + 0.05545 \dots y^{2} + 2.05476 \dots y + 7.74831 \dots \approx 0

Find one solution for

0.00694 \dots y^{3} + 0.05545 \dots y^{2} + 2.05476 \dots y + 7.74831 \dots = 0

using Newton-Raphson:

y \approx - 3.98565 \dots

Apply long division:

\frac{0.00694 \dots y ^{3} + 0.05545 \dots y ^{2} + 2.05476 \dots y + 7.74831 \dots}{y + 3.98565 \dots} = 0.00694 \dots y^{2} + 0.02777 \dots y + 1.94404 \dots

0.00694 \dots y^{2} + 0.02777 \dots y + 1.94404 \dots \approx 0

Find one solution for

0.00694 \dots y^{2} + 0.02777 \dots y + 1.94404 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solutions are

y \approx - 0.01434 \dots, y \approx - 3.98565 \dots

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