Question

Solve this quadratic equation. x^2 + 5x + 3 = 0

Answer 1

Hi there!
The question gives us the quadratic equation $x^{2} +5x+3=0$, and it tells us to solve it using the quadratic formula, which goes as $x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$. However, we must first find the values of a, b, and c. The official quadratic equation goes as $ax^2+bx+c$, which matches the format of the given quadratic equation. Hence, the value of a would be 1, the value of b would be 5, and the value of c would be 3. Now, just plug it back into the quadratic equation and simplify to get the zeros of the equation. 
$x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$
$x = \frac{-(5) \pm \sqrt{(5)^2 - 4(1)(3)} }{2(1)}$
$x = \frac{-5 \pm \sqrt{25 - 12} }{2}$
$x = \frac{-5 \pm \sqrt{13} }{2}$
$x = \frac{-5 \pm 3.61 }{2}$
$x = \frac{-5 + 3.61 }{2}, x = \frac{-5 - 3.61 }{2}$
$x=-0.695 \ \textgreater \ \ \textgreater \ -0.7, x= -4.305 \ \textgreater \ \ \textgreater \ x=-4.31$
Therefore, the solutions to the quadratic equation $x^{2} +5x+3=0$ are x = -0.7 and x = -4.31. Hope this helped and have a phenomenal day!