Indicate the correct solution to the quadratic equation below or whether there is no solution. \( x^{2}+5 x=6 \) Select one: \( x=6 \) and -1 no solution \( x=3 \) and -2 \( x=-6 \) and 1

To solve the equation \( x^{2}+5x-6=0 \), we first rearrange it to standard form. Factoring gives us \( (x+6)(x-1)=0 \), indicating the solutions \( x=-6 \) and \( x=1 \). So, the correct answer is \( x=-6 \) and \( x=1 \). Did you know that quadratic equations can often represent real-world phenomena? For example, they can model projectile motion, like a ball thrown in the air, where the coefficients describe the height and gravity's influence. The solutions to these equations help determine where the ball will hit the ground! When solving quadratics, a common mistake is overlooking factoring completely or mislabeling the roots. Remember to always check your factored form by multiplying back to ensure accuracy. If factoring seems tricky, don’t shy away from using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) for additional help!