/*! 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} Q.9.18 Solve (2t-8)2=-10... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Solve(2t-8)2=-10

Short Answer

Expert verified

The solutions of the quadratic equationt=4+i52,t=4-i52

Step by step solution

01

Step 1. Given information

Consider the quadratic equation

(2t-8)2=-10

Use the Square Root Property and simplify the radical.

Ifx2=k, thenx=±k

(2t-8)=±-10(2t-8)=±10i

Add 8 to both sides.

2t=±10i+8

Divide both sides by 2.

localid="1645460079112" t=±10i+82

Rewrite in standard form.

localid="1645460187619" t=±10i2+82t=±5·2i2+4t=±52i+4

Rewrite to show two solutions.

localid="1645460289551" t=52i+4,t=-52i+4

02

Step 2. Check for solutions.

Substitute t=52i+4in the original equation.

(2t-8)2=-10252i+4-82=?-10-2-8=?-10-10=-10

Substitute t=-52i+4in the original equation.

(2t-8)2=-102-52i+4-82=?-10-2-8=?-10-10=-10

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 91Ó°ÊÓ!

One App. One Place for Learning.

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

Get started for free

Study anywhere. Anytime. Across all devices.