Solve the equation.

8 x squared minus 56 x minus 144 equals 0
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Part 1
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1 answer

To solve the quadratic equation \( 8x^2 - 56x - 144 = 0 \), we can use the quadratic formula, which is given by:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

In this equation, the coefficients are:

  • \( a = 8 \)
  • \( b = -56 \)
  • \( c = -144 \)
  1. First, we calculate the discriminant \( b^2 - 4ac \):

\[ b^2 = (-56)^2 = 3136 \] \[ 4ac = 4 \times 8 \times (-144) = -4608 \] \[ b^2 - 4ac = 3136 - (-4608) = 3136 + 4608 = 7744 \]

  1. Now we can use the quadratic formula:

\[ x = \frac{-(-56) \pm \sqrt{7744}}{2 \times 8} \] \[ x = \frac{56 \pm 88}{16} \]

  1. Calculate the two possible solutions for \( x \):
  • First solution: \[ x = \frac{56 + 88}{16} = \frac{144}{16} = 9 \]

  • Second solution: \[ x = \frac{56 - 88}{16} = \frac{-32}{16} = -2 \]

Thus, the two solutions for the equation \( 8x^2 - 56x - 144 = 0 \) are:

\[ x = 9, -2 \]

So you can enter your response as:

\[ \text{x equals } 9, -2 \]