Question

use the quadratic formula to find the solutions for y = -x² - 5x + 12 options: no real solution, \\(\frac{-5 pm sqrt{73}}{-2}\\), \\(\frac{5 pm sqrt{73}}{-2}\\), \\(\frac{5 pm sqrt{73}}{2}\\)

Explanation:

Step1: Set equation to 0

$-x^2 -5x +12 = 0$

Step2: Identify a,b,c

$a=-1,\ b=-5,\ c=12$

Step3: Apply quadratic formula

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

Step4: Substitute values

$x=\frac{-(-5) \pm \sqrt{(-5)^2-4(-1)(12)}}{2(-1)}$

Step5: Simplify expression

$x=\frac{5 \pm \sqrt{25+48}}{-2}=\frac{5 \pm \sqrt{73}}{-2}$

Answer:

$\frac{5 \pm \sqrt{73}}{-2}$