[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
- Solve using the quadratic formula ⇨ x² - 2x - 48 = 0.
[tex] \large \boxed{\mathbb{ANSWER \: WITH \: EXPLANATION} \downarrow}[/tex]
[tex] \sf \: x ^ { 2 } - 2 x - 48 = 0[/tex]
All equations of the form ax² + bx + c = 0 can be solved using the quadratic formula: [tex]\sf \frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
[tex] \sf \: x^{2}-2x-48=0 [/tex]
This equation is in standard form: ax² + bx + c = 0 Substitute 1 for a, -2 for b and -48 for c in the quadratic formula.
[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-48\right)}}{2} \\ [/tex]
Square -2.
[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{4-4\left(-48\right)}}{2} \\ [/tex]
Multiply -4 times -48.
[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{4+192}}{2} \\ [/tex]
Add 4 to 192.
[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{196}}{2} \\ [/tex]
Take the square root of 196.
[tex] \sf \: x=\frac{-\left(-2\right)±14}{2} \\ [/tex]
The opposite of -2 is 2.
[tex] \sf \: x=\frac{2±14}{2} \\ [/tex]
Now solve the equation [tex]\sf\:x=\frac{2±14}{2}[/tex] when ± is plus. Add 2 to 14.
[tex] \sf \: x=\frac{16}{2} \\ [/tex]
Divide 16 by 2.
[tex] \boxed{ \boxed{ \bf \: x=8 }}[/tex]
Now solve the equation [tex]\sf\:x=\frac{2±14}{2} [/tex] when ± is minus. Subtract 14 from 2.
[tex] \sf \: x=\frac{-12}{2} \\ [/tex]
Divide -12 by 2.
[tex] \boxed{\boxed{ \bf \: x=-6 }}[/tex]
The equation is now solved.
[tex] \underline{ \bf \: x=8 }\\ \underline{ \bf \: x=-6 }[/tex]
