# solving equations but they get increasingly awesome | Summary and Q&A

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June 1, 2022
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blackpenredpen
solving equations but they get increasingly awesome

## TL;DR

Learn how to solve polynomial equations of different degrees using various methods and discover the beauty of complex numbers.

## Key Insights

• ❓ Linear equations can be solved by isolating the variable.
• ❎ Quadratic equations can be solved by completing the square.
• ❓ Cubic equations can be solved by factoring.
• 🗂️ Quartic equations can be solved by dividing by x^2 and factoring.
• ❓ There is no general formula to solve quintic equations.
• 🫚 Complex numbers can be used to find the roots of equations.
• 💁 Complex numbers have a polar form and can be written using Euler's formula.

## Transcript

Solving polynomial equations but they get increasingly awesome level one here we have this linear equation  x+1=0 we can just move the 1 to the other   side and we get x is equal to negative  1 and then we are done good level 2.   so now we have a quadratic equation x^2+x+1=0.  well let's go ahead and do this by completing a   square first move the... Read More

### Q: How do you solve linear equations?

To solve linear equations, isolate the variable by moving constants to the other side of the equation. For example, in the equation x + 1 = 0, subtract 1 from both sides to get x = -1.

### Q: How do you solve quadratic equations by completing the square?

To solve quadratic equations by completing the square, move the constant term to the other side of the equation. Find the "magic number" (half the coefficient of x squared) and add it to both sides. Take the square root of both sides and solve for x.

### Q: Can cubic equations be solved by factoring?

Yes, cubic equations can be solved by factoring. Group the terms and factor out the common factor. Set each factor equal to zero and solve for x.

### Q: How can quartic equations be solved without using the quartic formula?

Quartic equations can be solved by dividing by x^2 and factoring. Divide each term individually and factor out the common factor. Solve the resulting quadratic equation to find the possible values of x.

## Summary & Key Takeaways

• The content teaches how to solve linear equations by isolating the variable.

• The content demonstrates how to solve quadratic equations by completing the square.

• The content explains how to solve cubic and quartic equations by factoring and using special methods.