Question

Solve the equations below. Give exact solutions only. Show your work.

Answer 1

Step-by-step explanation:

remember, the general formula to solve a quadratic equation ax² + bx + c = 0 is

x = (-b ± sqrt(b² - 4ac))/(2a)

a)

I think there is a typo, and this should be

5x² - 7x = 72

5x² -7x - 72 = 0

x = (7 ± sqrt(49 - -1440))/10 = (7 ± sqrt(1489))/10

x1 = (7 + sqrt(1489))/10

x2 = (7 - sqrt(1489))/10

b)

x(x + 2) = 5

x² + 2x - 5 = 0

x = (-2 ± sqrt(4 - -20))/2 = (-2 ± sqrt(24))/2 =

= (-2 ± sqrt(4×6))/2 = (-2 ± 2×sqrt(6))/2 =

= -1 ± sqrt(6)

x1 = -1 + sqrt(6)

x2 = -1 - sqrt(6)

c)

3x² + 2x - 4 = 0

x = (-2 ± sqrt(4 - -48))/6 = (-2 ± sqrt(52))/6 =

= (-2 ± sqrt(4×13))/6 = (-2 ± 2×sqrt(13))/6 =

= (-1 ± sqrt(13))/3

x1 = (-1 + sqrt(13))/3

x2 = (-1 - sqrt(13))/3