✏️ QUADRATIC EQUATION
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SOLUTION
Solving quadratic equations using the quadratic formula
1. Determine the quadratic equation’s coefficients A, B, and C
[tex]a=1\\b=-4\\c=- 6[/tex]
2. Plug these coefficients into the quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\\\\x=\frac{-1-4\pm\sqrt{-4^2-41-6} }{2^.1}[/tex]
Simplify exponents and square roots
[tex]x=\frac{-1-4\pm\sqrt{16-41-6} }{21}[/tex]
Perform any multiplication or division, from left to right:
[tex]x=\frac{-1^.-4\pm\sqrt{16-4^.-6} }{2^.1}\\\\x=\frac{-1^.-4\pm\sqrt{16--24} }{2^.1} \\\\x=\frac{-1^.-4\pm\sqrt{16+24} }{2^.1} \\\\x=\frac{-1^.-4\pm\sqrt{40} }{2} \\\\x=\frac{4\pm\sqrt{40} }{2}[/tex]
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Group the prime factors into pairs and rewrite them in exponent form:
4. Solve the equation for x
[tex]x_1=\frac{4+2^.\sqrt{10} }{2} \\\\x_1=\frac{4+2^.3.162}{2}[/tex]
[tex]x_1=\frac{4+6.325}{2} \\\\x_1=\frac{10.325}{2} \\\\x_1=5.162\\\\x_2=\frac{4-2^.\sqrt{10} }{2} \\\\x_2=\frac{4-2^.3.162}{2} \\\\[/tex]
Perform any multiplication or division, from left to right:
[tex]x_2=\frac{4-2^.3.162}{2} \\\\x_2=\frac{4-6.325}{2} \\\\x_2=\frac{-2.325}{2} \\\\x_2=-1.162[/tex]
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THE RESULT IS
[tex]x_1=5.162\\\\x_2=1.162[/tex]
[tex]\huge\pink{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]
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