Question

X²−8x=38. Spell all words correctly, and use numerals instead of words.

a) x=−3 or x=11
b) x=3 or x=−11
c) x=−3 or x=−11
d) x=3 or x=11

Answer 1

To solve the equation x² - 8x = 38, we can use the quadratic formula. The solutions are x = 4 + 3√6 and x = 4 - 3√6.

Step-by-step explanation:

To solve the equation x² − 8x = 38, we can rearrange it as x² − 8x - 38 = 0. This is a quadratic equation in the form ax² + bx + c = 0, where a = 1, b = -8, and c = -38. We can use the quadratic formula to find the solutions:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values, we get:

x = (8 ± √((-8)² - 4(1)(-38))) / (2(1))

x = (8 ± √(64 + 152)) / 2

x = (8 ± √216) / 2

x = (8 ± √(6² × 6)) / 2

x = (8 ± 6√6) / 2

x = 4 ± 3√6

So the solutions are x = 4 + 3√6 and x = 4 - 3√6.