/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 23 Solve. $$ (x-4)(x-4)=0 $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 23

Solve. $$ (x-4)(x-4)=0 $$

Short Answer

Expert verified
x = 4.

Step by step solution

01

Write the equation

The original equation given is: (x - 4)(x - 4) = 0.
02

Simplify the equation

Recognize that (x - 4)(x - 4) is the same as (x - 4)^2. Rewrite the equation as: (x - 4)^2 = 0.
03

Solve for x

To solve (x - 4)^2 = 0, take the square root of both sides of the equation. This gives: x - 4 = 0.
04

Isolate x

Add 4 to both sides to isolate x: x = 4.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Factoring Quadratics
In algebra, factoring quadratics is a method used to solve quadratic equations of the form ax^2 + bx + c = 0. Factoring involves breaking down the quadratic equation into the product of two binomials. For example, the given equation (x - 4)(x - 4) = 0 is already factored for us. Each factor represents a possible solution to the equation.
  • If (a)(b) = 0, then either a = 0 or b = 0.
  • In this case, (x - 4) is both a and b.
  • By setting each factor to zero, we get x - 4 = 0.
Factoring is useful when you want to find the roots of a quadratic equation quickly.
Simplifying Equations
Simplifying equations makes them easier to solve. In our example, we start with (x - 4)(x - 4) = 0. We can recognize that (x - 4)(x - 4) is actually (x - 4)^2.
  • This shows that we are dealing with a perfect square trinomial.
  • We rewrite the equation as (x - 4)^2 = 0.
Rewriting it this way simplifies our process because now we can directly apply the next steps to solve for x.
Isolating Variables
Isolation of variables is crucial for solving equations. To solve (x - 4)^2 = 0, take the square root of both sides. This isolates our variable inside the equation.
  • We get x - 4 = 0.
  • Our next goal is to have x all by itself on one side of the equation.
To isolate x, you need to undo whatever operations are affecting it. In this case, subtracting 4 from x.
Square Root Method
The square root method is particularly useful for dealing with squared terms like (x - 4)^2. This method involves taking the square root of both sides to simplify the equation.
  • For example, (x - 4)^2 = 0 simplifies to x - 4 = 0 when you take the square root of both sides.
  • After applying the square root, we solve the resulting linear equation. Add 4 to both sides to isolate x and get x = 4.
This method helps simplify the problem by reducing it from a quadratic to a linear equation.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Use a pattern to factor \(25 z^{2}+9\). Incorrect Answer: Since the pattern is \(a^{2}+b^{2}=\) \((a+b)(a+b), a=5 z\) and \(b=3\), and the factored polynomial is \((5 z+3)(5 z+3)\).

Factor completely. Identify any prime polynomials. $$ 300 d^{3}-48 d k^{2} $$

Solve. $$ (p+4)(p-7)=0 $$

Solve. $$ -5(x-3)(x-7)=0 $$

Factor completely. Identify any prime polynomials. $$ 2 x^{2}+36 x+162 $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.