Solve the following quadratic equation using the quadratic formula.

5x^2 - 8x + 5 = 0

Write the solutions in the following form, where r, s, and t are integers, and the fractions are in simplest form.

x = r - si/t, x = r + si/t

Step-by-step explanation:

a = 5; b = - 8; c = 5

b² - 4ac = (-8) ² - 4 * 5 * 5 = 64 - 100 = (-36) < 0

x = - b ± √ (4ac - b²) i / 2a

= - (-8) ±√ 4 * 5 * 5 - (-8) ² i / 2 * 5

= 8 ± √36 i

10

= 8 ± 6 i

10

= 2 (4 ± 3i) = 4 ± 3i

10 5

= 4 ± 3i

5 5

x = 4/5 + 3i/5; x = 4/5 - 3i/5

Step-by-step explanation:

5x² - 8x + 5 = 0

delta = b² - 4ac a = 5 and b = - 8 and c=5

delta = (-8) ² - 4 (5) (5) = 64 - 100 = - 36 = (6i) ². i² = - 1

x1 = (8-6i) / 10 = (4-3i) / 5

x2 = (8+6i) / 10 = (4+3i) / 5

so r=4 and s=3 and t = 5