What are the solutions to the equation 2a^2-a-2=0.8a^6-13a^3-3 ?

The solutions to the equation 2a^2-a-2=0.8a^6-13a^3-3 are a\approx 2.57656…,a\approx-0.54657…

Find the zeros of 2a^2-a-2=0.8a^6-13a^3-3

The zeros of 2a^2-a-2=0.8a^6-13a^3-3 are a\approx 2.57656…,a\approx-0.54657…

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Popular Algebra >

2a^2-a-2=0.8a^6-13a^3-3

Solution

2 a^{2} - a - 2 = 0.8 a^{6} - 13 a^{3} - 3

Solution

a \approx 2.57656 \dots, a \approx - 0.54657 \dots

Solution steps

2 a^{2} - a - 2 = 0.8 a^{6} - 13 a^{3} - 3

Multiply both sides by

10

20 a^{2} - 10 a - 20 = 8 a^{6} - 130 a^{3} - 30

Switch sides

8 a^{6} - 130 a^{3} - 30 = 20 a^{2} - 10 a - 20

Move

20

to the left side

8 a^{6} - 130 a^{3} - 10 = 20 a^{2} - 10 a

Move

10 a

to the left side

8 a^{6} - 130 a^{3} - 10 + 10 a = 20 a^{2}

Move

20 a^{2}

to the left side

8 a^{6} - 130 a^{3} - 10 + 10 a - 20 a^{2} = 0

Write in the standard form

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

8 a^{6} - 130 a^{3} - 20 a^{2} + 10 a - 10 = 0

Find one solution for

8 a^{6} - 130 a^{3} - 20 a^{2} + 10 a - 10 = 0

using Newton-Raphson:

a \approx 2.57656 \dots

Apply long division:

\frac{8 a ^{6} - 130 a ^{3} - 20 a ^{2} + 10 a - 10}{a - 2.57656 \dots} = 8 a^{5} + 20.61254 \dots a^{4} + 53.10962 \dots a^{3} + 6.84056 \dots a^{2} - 2.37481 \dots a + 3.88113 \dots

8 a^{5} + 20.61254 \dots a^{4} + 53.10962 \dots a^{3} + 6.84056 \dots a^{2} - 2.37481 \dots a + 3.88113 \dots \approx 0

Find one solution for

8 a^{5} + 20.61254 \dots a^{4} + 53.10962 \dots a^{3} + 6.84056 \dots a^{2} - 2.37481 \dots a + 3.88113 \dots = 0

using Newton-Raphson:

a \approx - 0.54657 \dots

Apply long division:

\frac{8 a ^{5} + 20.61254 \dots a ^{4} + 53.10962 \dots a ^{3} + 6.84056 \dots a ^{2} - 2.37481 \dots a + 3.88113 \dots}{a + 0.54657 \dots} = 8 a^{4} + 16.23993 \dots a^{3} + 44.23325 \dots a^{2} - 17.33629 \dots a + 7.10080 \dots

8 a^{4} + 16.23993 \dots a^{3} + 44.23325 \dots a^{2} - 17.33629 \dots a + 7.10080 \dots \approx 0

Find one solution for

8 a^{4} + 16.23993 \dots a^{3} + 44.23325 \dots a^{2} - 17.33629 \dots a + 7.10080 \dots = 0

using Newton-Raphson:

No Solution for

a \in R

The solutions are

a \approx 2.57656 \dots, a \approx - 0.54657 \dots

Graph

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x^{10}=-x

x^{10} = - x

-x^3+9x^2-24x+20=0

- x^{3} + 9 x^{2} - 24 x + 20 = 0

(x^2-8)^2-2(x^2-8)+1=0

(x^{2} - 8)^{2} - 2 (x^{2} - 8) + 1 = 0

-4x^5=256x^2

- 4 x^{5} = 256 x^{2}

Frequently Asked Questions (FAQ)

What are the solutions to the equation 2a^2-a-2=0.8a^6-13a^3-3 ?
The solutions to the equation 2a^2-a-2=0.8a^6-13a^3-3 are a\approx 2.57656…,a\approx-0.54657…
Find the zeros of 2a^2-a-2=0.8a^6-13a^3-3
The zeros of 2a^2-a-2=0.8a^6-13a^3-3 are a\approx 2.57656…,a\approx-0.54657…

2a^2-a-2=0.8a^6-13a^3-3

Solution

Solution

Graph

Popular Examples

Frequently Asked Questions (FAQ)

What are the solutions to the equation 2a^2-a-2=0.8a^6-13a^3-3 ?

Find the zeros of 2a^2-a-2=0.8a^6-13a^3-3

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