Algebra assignment solution

Please solve the following problems:

  1. Solve for x

X2+x-12=0

SOLUTION

X2+x-12=0

To solve for x in above problem we will calculate the real roots for the above quadratic equations by looking for two numbers whose sum is 1 and product is 12, then we equate them in the original equation and solve for x.

Sum = 1, product = 12 the two numbers are 4 and -3

We equate to have x2+4x-3x-12=0

X(x+4)-3(x+4) = 0 thus x+4=0 and X= -4

OR X-3=0 AND X=3 thus x = 3 or -4

  1. Solve for x 22x-4=64

SOLUTION

Too solve for x we first equate the two values on both sides to the same base (base 2) then since the two are equal and with same base then their powers are equal thus we equate the powers and solve

Solve for x 22x-4=64 note 64=26

22x-4=26 thus 2x-4=6, collect like terms together

2x= 6+4

2x=10 and diving by 2 both sides

2x/2 = 10/2, x=5

X=5

  1. Solve for x

3cosx +2sin2x=0

Solution

3cosx +2sin2x=0

To solve for x we will use the trigonometric inequality stating that cos2x + sin2x =1 thus sin2x=1-cos2x thus we replace sin2x with

1-cos2x to have

3cosx+2(1-cos2x) =0, 3cosx+2-2cos2x = 0, let cos x be y

3y-2y2+2=0, -2y2=3y+2=0 then we solve the quadratic equation

Sum 3, product= -4 the two numbers are 4 and -1

-2y2+4y-y+2=0 , -2y(y-2)-1(y-2) =0 ,(-2y-1)(y-2)=0

We equate in (-2y-1)=0 ,y=-1/2 or y-2=0 ,y=2

So -2y = -1, y= -1/2 or y-2=0 , y=2 recall y= cosx thus cosx=2

Recall y= cos (x) thus y=cos x = -1/2 or 2

x=cos-1 2 which is absurd

X= cos-1 -1/2 = 120 or 240

Thus value of x is120, x=120 or x = 240

Want latest solution of this assignment

+ Submit Your Assignment Here

AssignmentHippo Features

On Time Delivery

Our motto is deliver assignment on Time. Our Expert writers deliver quality assignments to the students.

Plagiarism Free Work

Get reliable and unique assignments by using our 100% plagiarism-free.

24 X 7 Live Help

Get connected 24*7 with our Live Chat support executives to receive instant solutions for your assignment.

Services For All Subjects

Get Help with all the subjects like: Programming, Accounting, Finance, Engineering, Law and Marketing.

Best Price Guarantee

Get premium service at a pocket-friendly rate at AssignmentHippo

FREE SAMPLE FILE

Client Review

I was struggling so hard to complete my marketing assignment on brand development when I decided to finally reach to the experts of this portal. They certainly deliver perfect consistency and the desired format. The content prepared by the experts of this platform was simply amazing. I definitely owe my grades to them.

Tap to Chat
Get instant assignment help