2sin^2 (x) -5 sin (x) -3=0 i. rewrite  the  equation  by  substituting  the  expression  u  in  for  sin x. ii. factor  the  quadratic  expression.  rewrite  the  equation  with  factors  instead  of  the  original polynomial. iii. use  the  zero  product  property  to  solve  the  quadratic  equation. iv. rewrite  your  solutions  to  part  iii  by  replacing  u  with  sin x. v. solve  the  remaining  equations  for  x,  giving  all  solutions  to  the  equation.

we have that

I. Rewrite the equation by substituting the expression u in for sin x.

II. Factor the quadratic expression. Rewrite the equation with factors instead of the original polynomial.

is equal to

using a graph calculator-----> see the attached figure

III. Use the zero product property to solve the quadratic equation.

(u-3)=0--------------> u=3

(2u+1)=0-------- 2u=-1------> u=-1/2-----> u=-0.5

IV. Rewrite your solutions to Part III by replacing u with sin x.

sin x=3--------> is not the solution (sin x can not be greater than 1)

sin x=-0.50------>is the solution

V. Solve the remaining equations for x, giving all solutions to the equation.

sin x=-0.50

if the sine is negative

then

x belong to the III or IV quadrant

we know that

sin 30°=0.50

so

the solution for the III quadrant is

x=180°+30°-------> x=210°

the solution for the IV quadrant is

x=360°-30°------> x=330°

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

47 - 90 = 43

43 - 180 = x

x = 137