\( 8 \quad - x ^ { 2 } + 8 = 7 x \)

To solve the equation \( 8 - x^2 + 8 = 7x \), we can first simplify it. Combine like terms on the left side: \[ 16 - x^2 = 7x \] Rearranging gives us: \[ -x^2 - 7x + 16 = 0 \] Multiplying the entire equation by -1 to make the leading coefficient positive: \[ x^2 + 7x - 16 = 0 \] Now, you can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 1, b = 7, c = -16 \). The discriminant \( b^2 - 4ac = 7^2 - 4(1)(-16) = 49 + 64 = 113 \), which is positive, indicating two real and distinct solutions. Plugging the values into the formula gives us: \[ x = \frac{-7 \pm \sqrt{113}}{2} \] This will give you the two solutions for \( x \)! Now, won't that be an adventure in solving quadratics? Now, if you ever feel overwhelmed by quadratic equations, just remember that they're like a puzzle! Many students err by forgetting to check their discriminant before diving into solutions. Always ensure your equation is arranged neatly before applying formulas to avoid those pesky mistakes. Happy calculating!