Question

Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth. a2 − 28a 192 = 0 –8, –24 8, 24 –12, –16 12, 16

Answer 1

The solutions to the quadratic equation a2 − 28a + 192 = 0 are x = 16 and x = 12, found by applying the quadratic formula without the need for rounding.

Step-by-step explanation:

To solve the quadratic equation a2 − 28a + 192 = 0 using the quadratic formula, we first identify the coefficients of the equation which are a = 1, b = -28, and c = 192. The quadratic formula is given by x = (-b ± √(b2 - 4ac)) / (2a). Applying this formula, we have:

x = (28 ± √((-28)2 - 4*1*192)) / (2*1)

x = (28 ± √(784 - 768)) / 2

x = (28 ± √16) / 2

x = (28 ± 4) / 2

So the two possible solutions for x are:

x = (28 + 4) / 2 = 32 / 2 = 16

and

x = (28 - 4) / 2 = 24 / 2 = 12

Therefore, the solutions to the equation are x = 16 and x = 12. We do not need to round as the solutions are exact whole numbers.