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:
- \( a = 8 \)
- \( b = -56 \)
- \( c = -144 \)
- First, we calculate the discriminant \( b^2 - 4ac \):
\[ b^2 = (-56)^2 = 3136 \] \[ 4ac = 4 \times 8 \times (-144) = -4608 \] \[ b^2 - 4ac = 3136 - (-4608) = 3136 + 4608 = 7744 \]
- Now we can use the quadratic formula:
\[ x = \frac{-(-56) \pm \sqrt{7744}}{2 \times 8} \] \[ x = \frac{56 \pm 88}{16} \]
- 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:
\[ \text{x equals } 9, -2 \]