Determine whether the values −1 and 73 are solutions to the quadratic equation 3x2−4x−4=3.(1 point)

1 answer

To determine if the values \(-1\) and \(73\) are solutions to the quadratic equation \(3x^2 - 4x - 4 = 3\), we first need to rearrange the equation into standard form by moving \(3\) to the left side:

\[ 3x^2 - 4x - 4 - 3 = 0 \] \[ 3x^2 - 4x - 7 = 0 \]

Now we can substitute \(-1\) into the equation:

  1. Substituting \(x = -1\):

\[ 3(-1)^2 - 4(-1) - 7 = 0 \] \[ 3(1) + 4 - 7 = 0 \] \[ 3 + 4 - 7 = 0 \] \[ 0 = 0 \quad \text{(True)} \]

Thus, \(-1\) is a solution to the equation.

  1. Substituting \(x = 73\):

\[ 3(73)^2 - 4(73) - 7 = 0 \] Calculating \(73^2\): \[ 73^2 = 5329 \] Now substitute:

\[ 3(5329) - 4(73) - 7 = 0 \] \[ 15987 - 292 - 7 = 0 \] Now perform the subtraction:

\[ 15987 - 292 = 15695 \] Then,

\[ 15695 - 7 = 15688 \neq 0 \]

Thus, \(73\) is not a solution to the equation.

In conclusion:

  • \(-1\) is a solution.
  • \(73\) is not a solution.