/*! 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 119 Solve each radical equation. Che... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 119

Solve each radical equation. Check all proposed solutions. $$\sqrt{2 x+13}=x+7$$

Short Answer

Expert verified
The solution to the equation is x = -6

Step by step solution

01

Isolate the square root term

The first step is to isolate the radical term on one side of the equation. However, in our equation, this is already done for us. Our equation is already in the form \(\sqrt{2x+13} = x + 7\).
02

Square both sides of the equation

Since we have a square root, the next step is to square both sides of the equation. (Note: squaring the square root of a number cancels it out) The equation then becomes: \((2x+13) = (x + 7)^2\.
03

Expand the square

The next step is to simplify the equation by expanding \((x + 7)^2\) to \(x^2 + 14x + 49\) and subtract 2x and subtract 13 from both sides. This gives us \Our equation now looks like this: \(x^2 + 12x + 36 = 0\)
04

Factor the quadratic equation

Factor the quadratic equation on both sides. This will help you find solutions to the equation. The factored form of the equation is \((x+6)^2 = 0\)
05

Solve for x

In this step, solve for x by setting the factor equal to zero. So, we get x+6=0 which gives us x=-6
06

Check the solution

The last step is to check the solution. Substitute the x value of -6 back into the original equation and see if it holds true. Substituting -6 into \(\sqrt{2x + 13} = x + 7\) results in \(\sqrt{2*(-6) + 13} = -6 + 7\) -> \(\sqrt{-12 + 13} =1\) -> \(\sqrt{1}=1\). Since both sides equal 1, the solution x=-6 is correct.

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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I prefer interval notation over set-builder notation because it takes less space to write solution sets.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A company manufactures and sells blank audiocassette tapes. The weekly fixed cost is \(\$ 10,000\) and it costs \(\$ 0.40\) to produce each tape. The selling price is \(\$ 2.00\) per tape. How many tapes must be produced and sold each week for the company to generate a profit?

If you are given a quadratic equation, how do you determine which method to use to solve it?

$$\text { Solve for } t: \quad s=-16 t^{2}+v_{0} t$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can check inequalities by substituting 0 for the variable: When 0 belongs to the solution set, I should obtain a true statement, and when 0 does not belong to the solution set. I should obtain a false statement.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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.