Question

2 z squared minus 21 z minus 36 equals 0

Answer 1

try again

Answer 2

factor

Answer 3

To solve this quadratic equation, we can use the quadratic formula:

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In the equation 2z^2 - 21z - 36 = 0, a = 2, b = -21, and c = -36.

Plugging these values into the formula, we get:

z = (21 ± √((-21)^2 - 4*2*(-36))) / (2*2)
z = (21 ± √(441 + 288)) / 4
z = (21 ± √729) / 4
z = (21 ± 27) / 4

Now, we have two possible solutions:
1. z = (21 + 27) / 4 = 48 / 4 = 12
2. z = (21 - 27) / 4 = -6 / 4 = -1.5

Therefore, the solutions to the equation 2z^2 - 21z - 36 = 0 are z = 12 and z = -1.5.

Answer 4

My apologies for the mistake. Let's solve the equation again.

Given equation: 2z^2 - 21z - 36 = 0

To solve this quadratic equation, we can factorize it or use the quadratic formula.

Using the quadratic formula: z = (-(-21) ± √((-21)^2 - 4*2*(-36))) / (2*2)
z = (21 ± √(441 + 288)) / 4
z = (21 ± √729) / 4
z = (21 ± 27) / 4

Now, we have two possible solutions:
1. z = (21 + 27) / 4 = 48 / 4 = 12
2. z = (21 - 27) / 4 = -6 / 4 = -1.5

Therefore, the correct solutions to the equation 2z^2 - 21z - 36 = 0 are z = 12 and z = -1.5.

Answer 5

To factor the quadratic equation 2z^2 - 21z - 36 = 0, we need to find two numbers that multiply to 72 (2*-36) and add up to -21 (the coefficient of the middle term).

The two numbers are -24 and 3 because -24 * 3 = -72 and -24 + 3 = -21.

Now we rewrite the middle term using these two numbers:
2z^2 - 24z + 3z - 36 = 0

Factor by grouping:
2z(z - 12) + 3(z - 12) = 0
(z - 12)(2z + 3) = 0

Now, set each factor to zero and solve for z:
z - 12 = 0
z = 12

2z + 3 = 0
2z = -3
z = -3/2

The solutions to the quadratic equation 2z^2 - 21z - 36 = 0 are z = 12 and z = -3/2.