joline is solving the equation 0 = x² - 5x - 4 using the quadratic formula. which value is the negative real…

joline is solving the equation 0 = x² - 5x - 4 using the quadratic formula. which value is the negative real number solution to her quadratic equation? round to the nearest tenth if necessary.\nquadratic formula: x = \\frac{-b\\pm\\sqrt{b² - 4ac}}{2a}\n-5.7\n-4\n-1\n-0.7

joline is solving the equation 0 = x² - 5x - 4 using the quadratic formula. which value is the negative real number solution to her quadratic equation? round to the nearest tenth if necessary.\nquadratic formula: x = \\frac{-b\\pm\\sqrt{b² - 4ac}}{2a}\n-5.7\n-4\n-1\n-0.7

Answer

Explanation:

Step1: Identify coefficients

For the quadratic equation $0 = x^{2}-5x - 4$, we have $a = 1$, $b=-5$, $c = - 4$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac=(-5)^{2}-4\times1\times(-4)=25 + 16=41$.

Step3: Apply the quadratic formula

$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{5\pm\sqrt{41}}{2}$. The two solutions are $x_1=\frac{5+\sqrt{41}}{2}$ and $x_2=\frac{5 - \sqrt{41}}{2}$.

Step4: Find the negative solution

We know that $\sqrt{41}\approx6.4$. Then $x_2=\frac{5 - 6.4}{2}=\frac{-1.4}{2}=-0.7$.

Answer:

$-0.7$