/*! 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 3 Solve each equation in Exercises... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 3

Solve each equation in Exercises \(1-14\) by factoring. $$x^{2}=8 x-15$$

Short Answer

Expert verified
The solution to the equation is \(x = 3, 5\).

Step by step solution

01

Write the equation in standard form

First, move all terms to one side of the equation to put it in standard form. Subtract \(8x\) from both sides and add \(15\) to both sides gives \(x^2 - 8x + 15 =0\)
02

Factoring

To factorize it, find two numbers that multiply to \(ac = 15\) and adds up to \(b = -8\). The numbers -3 and -5 satisfy both those conditions. Therefore, break down the -8x into -3x and -5x: \(x^2 - 3x - 5x + 15 =0\)
03

Factor by Grouping

Group the terms and factor by grouping: \(x(x - 3) - 5(x - 3) = 0\). Now, notice that \((x - 3)\) is a common factor. Factoring out gives \((x - 3)(x - 5) = 0\)
04

Solve for x

Set each factor to zero and solve for \(x\): From \(x - 3 = 0\), \(x = 3\), From \(x - 5 = 0\), \(x = 5\). So, the solution to the equation is \(x = 3, 5\)

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

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\sqrt{-64}-\sqrt{-25}$$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-4 x \geq 0 $$

In Exercises \(73-74\), use the method for solving quadratic inequalities to solve each higher-order polynomial inequality. $$ x^{3}+2 x^{2}-x-2 \geq 0 $$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x+4}{2 x-1} \leq 3 $$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}+2 x<0 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.