How do you solve #x^3+2x^2 = 2# ?
Use Cardano's method to find real root:
#x_1 = 1/3(2+root(3)(19+3sqrt(33))+root(3)(193sqrt(33)))#
and related Complex roots.
To make the task of solving the cubic simpler, we make the cubic simpler using a linear substitution known as a Tschirnhaus transformation.
We want to solve:
Then:
Use the quadratic formula to find:
and related Complex roots:
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To solve the equation (x^3 + 2x^2 = 2), you can follow these steps:

Subtract 2 from both sides to isolate the polynomial: [x^3 + 2x^2  2 = 0.]

Try to factor the polynomial. In this case, you can't factor it easily, so you may need to use other methods.

One method is to use numerical methods or graphing technology to approximate the roots.

Another method is to use the Rational Root Theorem, which states that any rational roots of the polynomial equation (a_nx^n + a_{n1}x^{n1} + ... + a_1x + a_0 = 0) must be of the form ±p/q, where p is a factor of the constant term (a_0) and q is a factor of the leading coefficient (a_n).

By trying various factors of 2 (the constant term) and 1 (the leading coefficient), you can find the rational roots of the polynomial.

Once you've found a root, you can use polynomial division or synthetic division to divide the polynomial by (x  \text{root}) to obtain a quadratic equation.

Solve the quadratic equation to find the remaining roots, which may be real or complex.

Thus, you find all the roots of the original equation.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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