Algebra: Solving 5x² = 45

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Questions and Answers

What is the importance of isolating $x^2$ in the equation $5x^2 = 45$?

Isolating $x^2$ allows for easier solving of the equation by simplifying it to $x^2 = 9$.

Do you agree with Noah's conclusion that $X=3$? Why or why not?

No, I disagree because he did not consider both positive and negative roots; the correct values should be $x = 3$ and $x = -3$.

What would be the correct process to solve the equation $5x^2 = 45$?

First, divide both sides by 5 to get $x^2 = 9$ and then take the square root to find $x = 3$ and $x = -3$.

Identify any errors in Noah's calculations.

<p>Noah correctly simplified to $x^2 = 9$, but he failed to consider both roots resulting from the square root.</p> Signup and view all the answers

Explain why understanding both roots of $x^2 = 9$ is essential in algebra.

<p>Understanding both roots ensures a complete solution set, which is important in various applications of algebra.</p> Signup and view all the answers

Flashcards

Solving an Equation

The process of isolating a variable by performing inverse operations on both sides of an equation to find its value.

Dividing Both Sides

To get rid of a coefficient, divide both sides of the equation by that coefficient.

Taking the Root

To find the value of a variable raised to a power, perform the inverse operation, which is taking the root.

Two Solutions

When taking the square root of a number, remember that there are two possible solutions: one positive and one negative.

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Missing Solution

Noah's solution is incorrect because he forgot to consider the negative square root of 9. While 3 squared is 9, -3 squared is also 9.

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Study Notes

Analysis of Noah's Solution

Noah's problem: Solve 5x² = 45
Noah's steps:
- 5x² = 45
- x² = 9
- x = 3
Evaluation of Noah's solution: Noah's result is incorrect, and his method contains a crucial error.
Detailed explanation: While the first step (dividing both sides by 5 to obtain x² = 9) is correct, the final step (taking the square root to obtain x = 3) overlooks a crucial point.
Correct approach to finding x:
- To solve for x, we need to find the values of x that satisfy the equation x² = 9.
- Taking the square root of both sides gives us x = ±√9.
- The square root of 9 is +3, or -3, not just 3.
- Therefore, the correct solutions are x = 3 and x = -3.
Conclusion Regarding Noah's Logic:
- Noah correctly isolates x², but then makes an incorrect assumption by not considering the positive and negative solutions.
Conclusion on Noah's work:
- His methodology is partially correct, but the solution is not. A complete solution requires considering the two possible root values of a squared variable.

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Description

This quiz analyzes Noah's solution to the equation 5x² = 45. Although Noah correctly isolates x², he fails to account for both positive and negative square roots. Dive into his methodology and uncover the complete solution.