Question

What are the solutions of 8x² = 6 + 22x? (Check all that apply)

A. x = -3
B. x = 0
C. x = 3
D. x = 6

Answer 1

To solve the equation 8x² = 6 + 22x, rearrange it to the form 8x² - 22x - 6 = 0 and then use the quadratic formula to calculate the solutions. Option C is correct.

Step-by-step explanation:

To find the solutions of the given equation, we can rearrange it to the form:

8x² - 22x - 6 = 0

Next, we can use the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions can be found using the formula:

x = (-b ± √(b² - 4ac)) / 2a

For the given equation, a = 8, b = -22, and c = -6. Plugging in these values, we can calculate the solutions:

x = (-(-22) ± √((-22)² - 4(8)(-6))) / (2(8))

x = (22 ± √(484 + 192)) / 16

x = (22 ± √(676)) / 16

x = (22 ± 26) / 16

Therefore, the solutions of the equation are:

x = -1/2 (for x = -0.5)

x = 3