I really need help with solving quadratics using the quadratic formula, if anybody could help me with these problems that would be awesome, i would like an explanation on how to do this.

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \dfrac{-(-14)\pm\sqrt{(-14)^2-4(1)(36)}}{2(1)}\\\\x = \dfrac{14 \pm \sqrt{196-144}}{2}\\\\x = \dfrac{14\pm\sqrt{52}}{2}\\\\x = \dfrac{14\pm7.21}{2}[/tex]

Separate into two cases:

[tex]a)\ x = \dfrac{14 - 7.21}{2}\implies x = \dfrac{6.79}{2}\implies x = 3.395\\\textsf{Nearest tenth: 3.4}\\\\ b)\x = \dfrac{14 + 7.21}{2}\implies x = \dfrac{21.21}{2}\implies x=10.605\\\textsf{Nearest tenth: 10.6}[/tex]

2. x² + 7x + 16 = 0

a = 1, b = 7, c = 16

Substitute the given values into the formula:

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \dfrac{-7\pm\sqrt{7^2-4(1)(16)}}{2(1)}\\\\x = \dfrac{-7 \pm \sqrt{49-64}}{2}\\\\x = \dfrac{-7 \pm \sqrt{-15}}{2}\\\\ x = \dfrac{-7 \pm i\sqrt{15}}{2}[/tex]

Imaginary number rule: For any positive real number "k", [tex]\sqrt{-k} = i\sqrt{k}[/tex]

Note: Two imaginary solutions indicate that the graph will not intersect the x-axis. As a result, it has no real roots.

Separate into two cases:
[tex]a)\ x = \dfrac{-7 - i\sqrt{15}}{2}\implies x = \dfrac{-7}{2} - \dfrac{i\sqrt{15}}{2}\\\\b)\ x = \dfrac{-7 + i\sqrt{15}}{2}$}\implies x = \dfrac{-7}{2}$} + \dfrac{i\sqrt{15}}{2}[/tex]

3. x² - 10x - 11 = 0

a = 1, b = -10, c = -11

Substitute the given values into the formula:

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \dfrac{-(-10)\pm\sqrt{(-10)^2-4(1)(-11)}}{2(1)}\\\\x = \dfrac{10\pm\sqrt{100+44}}{2}\\\\x = \dfrac{10\pm\sqrt{144}}{2}\\\\x = \dfrac{10\pm12}{2}[/tex]

Separate into two cases:

[tex]a)\ x = \dfrac{10 - 12}{2}\implies x = \dfrac{-2}{2}\implies x = -1\\\\ b)\ x = \dfrac{10 + 12}{2}\implies x = \dfrac{22}{2}\implies x = 11[/tex]

Learn more about quadratic equation here:

brainly.com/question/27729447