What are the solutions to the equation 9w^2+17w+12=3w^23w^2 ?

The solutions to the equation 9w^2+17w+12=3w^23w^2 are w\approx-0.82191…,w\approx 1.63082…

Find the zeros of 9w^2+17w+12=3w^23w^2

The zeros of 9w^2+17w+12=3w^23w^2 are w\approx-0.82191…,w\approx 1.63082…

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9 w^{2} + 17 w + 12 = 3 w^{2} 3 w^{2}

w \approx - 0.82191 \dots, w \approx 1.63082 \dots

Solution steps

9 w^{2} + 17 w + 12 = 3 w^{2} \cdot 3 w^{2}

Expand

3 w^{2} \cdot 3 w^{2} : 9 w^{4}

9 w^{2} + 17 w + 12 = 9 w^{4}

Switch sides

9 w^{4} = 9 w^{2} + 17 w + 12

Move

12

to the left side

9 w^{4} - 12 = 9 w^{2} + 17 w

Move

17 w

to the left side

9 w^{4} - 12 - 17 w = 9 w^{2}

Move

9 w^{2}

to the left side

9 w^{4} - 12 - 17 w - 9 w^{2} = 0

Write in the standard form

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

9 w^{4} - 9 w^{2} - 17 w - 12 = 0

Find one solution for

9 w^{4} - 9 w^{2} - 17 w - 12 = 0

using Newton-Raphson:

w \approx - 0.82191 \dots

Apply long division:

\frac{9 w ^{4} - 9 w ^{2} - 17 w - 12}{w + 0.82191 \dots} = 9 w^{3} - 7.39727 \dots w^{2} - 2.92003 \dots w - 14.59996 \dots

9 w^{3} - 7.39727 \dots w^{2} - 2.92003 \dots w - 14.59996 \dots \approx 0

Find one solution for

9 w^{3} - 7.39727 \dots w^{2} - 2.92003 \dots w - 14.59996 \dots = 0

using Newton-Raphson:

w \approx 1.63082 \dots

Apply long division:

\frac{9 w ^{3} - 7.39727 \dots w ^{2} - 2.92003 \dots w - 14.59996 \dots}{w - 1.63082 \dots} = 9 w^{2} + 7.28011 \dots w + 8.95252 \dots

9 w^{2} + 7.28011 \dots w + 8.95252 \dots \approx 0

Find one solution for

9 w^{2} + 7.28011 \dots w + 8.95252 \dots = 0

using Newton-Raphson:

No Solution for

w \in R

The solutions are

w \approx - 0.82191 \dots, w \approx 1.63082 \dots

x + x^{2} - x^{4} + x^{8} = 125

s^{3} + 6 s^{2} + 5 s + 30 = 0

49 x^{4} + 9 = 58 x^{2}

z^{8} = 8 1^{2}

(n - 2)^{3} = 512

What are the solutions to the equation 9w^2+17w+12=3w^23w^2 ?
The solutions to the equation 9w^2+17w+12=3w^23w^2 are w\approx-0.82191…,w\approx 1.63082…
Find the zeros of 9w^2+17w+12=3w^23w^2
The zeros of 9w^2+17w+12=3w^23w^2 are w\approx-0.82191…,w\approx 1.63082…