What are the solutions to the equation 11r+15=r^2r^2 ?

The solutions to the equation 11r+15=r^2r^2 are r\approx-1.18461…,r\approx 2.56373…

Find the zeros of 11r+15=r^2r^2

The zeros of 11r+15=r^2r^2 are r\approx-1.18461…,r\approx 2.56373…

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11 r + 15 = r^{2} r^{2}

r \approx - 1.18461 \dots, r \approx 2.56373 \dots

Solution steps

11 r + 15 = r^{2} r^{2}

Refine

11 r + 15 = r^{4}

Switch sides

r^{4} = 11 r + 15

Move

15

to the left side

r^{4} - 15 = 11 r

Move

11 r

to the left side

r^{4} - 15 - 11 r = 0

Write in the standard form

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

r^{4} - 11 r - 15 = 0

Find one solution for

r^{4} - 11 r - 15 = 0

using Newton-Raphson:

r \approx - 1.18461 \dots

Apply long division:

\frac{r ^{4} - 11 r - 15}{r + 1.18461 \dots} = r^{3} - 1.18461 \dots r^{2} + 1.40330 \dots r - 12.66237 \dots

r^{3} - 1.18461 \dots r^{2} + 1.40330 \dots r - 12.66237 \dots \approx 0

Find one solution for

r^{3} - 1.18461 \dots r^{2} + 1.40330 \dots r - 12.66237 \dots = 0

using Newton-Raphson:

r \approx 2.56373 \dots

Apply long division:

\frac{r ^{3} - 1.18461 \dots r ^{2} + 1.40330 \dots r - 12.66237 \dots}{r - 2.56373 \dots} = r^{2} + 1.37912 \dots r + 4.93902 \dots

r^{2} + 1.37912 \dots r + 4.93902 \dots \approx 0

Find one solution for

r^{2} + 1.37912 \dots r + 4.93902 \dots = 0

using Newton-Raphson:

No Solution for

r \in R

The solutions are

r \approx - 1.18461 \dots, r \approx 2.56373 \dots

x^{3} + 2 x^{2} - x - 1 = 0

(x^{2} + 2 x + 20)^{2} = 0

h^{3} = 1

x^{3} + 3 x^{2} + x - 3 = 0

0 = 36 x^{3} - 49 x

What are the solutions to the equation 11r+15=r^2r^2 ?
The solutions to the equation 11r+15=r^2r^2 are r\approx-1.18461…,r\approx 2.56373…
Find the zeros of 11r+15=r^2r^2
The zeros of 11r+15=r^2r^2 are r\approx-1.18461…,r\approx 2.56373…