Question

value: 3
solve
$x^2 + 5x + 9 = 5$
using the quadratic formula.
a. 4 and 1
b. -5 and -4
c. -4 and -1
d. 5 and 4

Explanation:

Step1: Rewrite to standard form

$x^2 + 5x + 9 - 5 = 0$ → $x^2 + 5x + 4 = 0$

Step2: Identify coefficients

$a=1$, $b=5$, $c=4$

Step3: Apply quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute values:
$x = \frac{-5 \pm \sqrt{5^2 - 4(1)(4)}}{2(1)}$

Step4: Calculate discriminant

$\sqrt{25 - 16} = \sqrt{9} = 3$

Step5: Solve for x

$x_1 = \frac{-5 + 3}{2} = \frac{-2}{2} = -1$
$x_2 = \frac{-5 - 3}{2} = \frac{-8}{2} = -4$

Answer:

c. -4 and -1