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$2.99

Model

Completion - **GPT-3.5 **(text-davinci-003)

Token size

223 ($0.00450 / call)

Example input

Solve the equation 0.1 x4 - 1.3 x2 + 3.6 = 0

Example output

Sure, I can help you solve the equation 0.1x^4 - 1.3x^2 + 3.6 = 0.
To solve for x, we will use the quadratic formula, which states that the solutions to a quadratic equation of the form ax^2 + bx + c = 0 are given by:
x = (-b ยฑ sqrt(b^2 - 4ac)) / 2a
However, the equation given is not quadratic. It is a quartic equation, meaning it has a degree of four. To solve it, we can use a technique called substitution.
Let's substitute a variable u for x^2. Then our equation becomes:
0.1u^2 - 1.3u + 3.6 = 0
Now we can use the quadratic formula to solve for u:
u = (-(-1.3) ยฑ sqrt((-1.3)^2 - 4(0.1)(3.6))) / 2(0.1)
Simplifying the expression under the square root, we get:
u = (1.3 ยฑ sqrt(1.69 - 1.44)) / 0.2
u = (1.3 ยฑ sqrt(0.25)) / 0.2
u = (1.3 ยฑ 0.5) / 0.2
So we have two possible solutions for u:
u1 = 9
u2 = 2
Now we can substitute back to solve for x:
For u1:
u1 = x^2
x^2 = 9
x = ยฑ3
For u2:
u2 = x^2
x^2 = 2
x = ยฑsqrt(2)
Therefore, the solutions to the original equation 0.1x^4 - 1.3x^2 + 3.6 = 0 are:
x = 3, -3, sqrt(2), -sqrt(2).
I hope this helps! Let me know if you have any questions.

ยฉ PromptBase 2024

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