Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

The Square Root Property

College Algebra

1. Equations & Inequalities

The Square Root Property

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1:29 minutes

Problem 79

Textbook Question

Solve each equation. See Example 7. (x-3)^2/5 = 4

Verified step by step guidance

Multiply both sides of the equation by 5 to eliminate the fraction: $ (x-3)^2 = 4 \times 5 $.

Simplify the right side of the equation: $ (x-3)^2 = 20 $.

Take the square root of both sides to solve for $ x-3 $: $ x-3 = \pm \sqrt{20} $.

Simplify $ \sqrt{20} $ to $ 2\sqrt{5} $, so $ x-3 = \pm 2\sqrt{5} $.

Solve for $ x $ by adding 3 to both sides: $ x = 3 \pm 2\sqrt{5} $.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. They can be solved using various methods, including factoring, completing the square, or applying the quadratic formula. In this context, the equation involves a squared term, indicating that it can be treated as a quadratic equation once simplified.

Square Roots

Square roots are the values that, when multiplied by themselves, yield the original number. In solving equations involving squares, such as (x-3)^2, taking the square root of both sides is a common step. This process introduces both positive and negative solutions, which must be considered to find all possible values of x.

Isolating Variables

Isolating variables is a fundamental algebraic technique used to solve equations. It involves rearranging the equation to get the variable of interest (in this case, x) on one side and all other terms on the opposite side. This process often includes operations like addition, subtraction, multiplication, and division, allowing for a clearer path to finding the solution.