Order of steps exercise example | Quadratic equations | Algebra I | Khan Academy

TL;DR

This video demonstrates how to solve the equation 3(x + 6)^2 = 75 by dividing both sides by 3, taking the square root of both sides, and subtracting 6 from both sides.

Transcript

Use the cards below to create a list of steps in order that will solve the following equation. 3 times x plus 6 squared is equal to 75. And I encourage you to pause this video now and try to figure it out on your own. Figure out which of these steps and in what order you would do to solve for x here. So I'm assuming you've given it a go. So let's t... Read More

Key Insights

• 🫚 The equation is solved by following three steps: divide by 3, take the square root, and subtract 6.
• 🙃 Dividing both sides by 3 is necessary to eliminate the coefficient of x.
• ❎ Taking the square root accounts for the squared term and introduces both positive and negative solutions.

Questions & Answers

Q: What is the first step to solve the equation 3(x + 6)^2 = 75?

The first step is to divide both sides of the equation by 3 to isolate the expression (x + 6)^2.

Q: Why is it important to divide both sides of the equation by 3?

Dividing by 3 ensures that the equation remains balanced since we can't perform operations on one side without doing the same to the other side.

Q: What is the next step after dividing both sides by 3?

The next step is to take the square root of both sides to eliminate the exponent and solve for (x + 6).

Q: What is the final step in solving the equation?

The final step is to subtract 6 from both sides to isolate x and find the possible values that satisfy the equation.

Summary & Key Takeaways

• The equation given is 3(x + 6)^2 = 75.

• The first step is to divide both sides of the equation by 3.

• Next, the square root of both sides is taken.

• Subtracting 6 from both sides gives the possible values for x.