Use 3x2 3x 21 to answer problems 1820 Leave solutions in s

Use 3x^2 + 3x = 21 to answer problems 18-20. Leave solutions in simplest radical form. Solve by completing the square. Show all work. Use the discriminant to find the number of unique real solutions. Show all calculations. Solve with the quadratic formula. Show all work.

Solution

18) 3x² +3x = 21

==> 3(x² +x) = 21

==> x² +x = 7

==> x² + x -7 = 0

==> x² + 2(x)(1/2) + (1/2)² - (1/2)² -7 = 0

==> (x + 1/2)² - 1/4 -7 = 0

==> (x + 1/2)² = 29/4

==> (x + 1/2) = 29/2 , -29/2

==> x = (29 -1)/2 , -(29 +1)/2

19) 3x² +3x = 21

==> x² + x -7 = 0

comparing it with ax² + bx + c = 0

==> a = 1 , b = 1 , c = -7

Discriminant D = b² -4ac = 1² - 4(1)(-7)

==> D = 1 + 28 = 29

as D > 0 , number of unique real solutions are two

20) quadratic formula ==> x = [-b +/- (b² -4ac)]/2(a)

==> x = [-1 + 29]/2(1) , [-1 - 29]/2(1)

==> x = (-1 + 29)/2 , -(1 + 29)/2