/*! 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 82 Explain how to solve \((x-1)^{2}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 82

Explain how to solve \((x-1)^{2}=16\) using the square root property.

Short Answer

Expert verified
The solutions to the equation \((x-1)^{2}=16\) are \(x=5\) and \(x=-3\).

Step by step solution

01

Isolate the squared term

In the given equation the squared term is already isolated, i.e., \((x-1)^{2}=16\).
02

Square Root Property

Now,apply the square root property by taking the square root of both sides. This gives us \(x-1 = \sqrt{16}\) and \(x-1 = -\sqrt{16}\). Remember, when we take the square root of both sides we need to consider both positive and negative roots.
03

Simplify Square Roots

Now simplify the square root of 16. The square root of 16 is 4. So, the equations become \(x-1=4\) and \(x-1=-4\).
04

Solve for x

To isolate x, add 1 to both sides in each equation. This gives two solutions: \(x=4+1=5\) and \(x=-4+1=-3\).

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!

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

If a parabola has two \(x\) -intercepts, explain how to find them.

Evaluate: \(125^{-4}\). (Section 8.6, Example 3)

A car was purchased for \(\$ 22,500\). The value of the car decreases by \(\$ 3200\) per year for the first seven years. Write a function \(V\) that describes the value of the car after \(x\) years, where \(0 \leq x \leq 7 .\) Then find and interpret \(V(3)\).

Use a graphing utility to solve \((x-1)^{2}-9=0\) Graph \(y=(x-1)^{2}-9\) in a \([-5,5,1]\) by \([-9,3,1]\) viewing rectangle. The equation's solutions are the graph's \(x\) -intercepts. Check by substitution in the given equation.

a. Use a graphing utility to graph \(y=2 x^{2}-82 x+720\) in a standard viewing rectangle. What do you observe? b. Find the coordinates of the vertex for the given quadratic equation. c. The answer to part (b) is \((20.5,-120.5) .\) Because the leading coefficient, 2 of \(y=2 x^{2}-82 x+720\) is positive, the vertex is a minimum point on the graph. Use this fact to help find a viewing rectangle that will give a relatively complete picture of the parabola. With an axis of symmetry at \(x=20.5,\) the setting for \(x\) should extend past this, so try Xmin \(=0\) and \(\mathrm{Xmax}=30 .\) The setting for \(y\) should include (and probably go below) the \(y\) -coordinate of the graph's minimum point, so try Ymin \(=-130 .\) Experiment with Ymax until your utility shows the parabola's major features. d. In general, explain how knowing the coordinates of a parabola's vertex can help determine a reasonable viewing rectangle on a graphing utility for obtaining a complete picture of the parabola.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.