/*! 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 128 Solve each equation. $$10 x-1=... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 128

Solve each equation. $$10 x-1=(2 x+1)^{2}$$

Short Answer

Expert verified
The solutions to the equation are \(x = 1\) and \(x = 0.5\).

Step by step solution

01

Expand the Square

Apply the formula \((a+b)^2 = a^2 + 2ab + b^2\) to \( (2x+1)^2 \) to get \( 4x^2 + 4x + 1 \). The equation now is \( 10x - 1 = 4x^2 + 4x + 1 \).
02

Rearrange the Equation

Rearrange the equation to the standard quadratic form \(ax^2 + bx + c = 0\). This results in \( 4x^2 - 6x + 2 = 0\) after subtracting \(10x\) and adding \(1\) to both sides.
03

Apply the Quadratic Formula

Use the quadratic formula to solve for \(x\), which is \( x = [-b \pm \sqrt{b^2 - 4ac}]/(2a)\). Plugging \( a = 4\), \( b = -6 \), and \( c = 2\) into the formula gives solutions \( x = 1\) and \( x = 0.5\).

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 \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$8^{-\frac{1}{4}}=-2$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The model \(P=-0.18 n+2.1\) describes the number of pay phones, \(P,\) in millions, \(n\) years after \(2000,\) so I have to solve a linear equation to determine the number of pay phones in 2010.

In Exercises \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{\sqrt{20}}{8}=\frac{\sqrt{10}}{4}$$

Rationalize the numerator. $$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{x^{2}-25}{x-5}=x-5$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Applied 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.