[tex] \large \green {\bold{PROBLEM:}}[/tex]
[tex] \large \bold{4x {}^{2} - 4x + 1 = 7}[/tex]
1.) bring the equation to the simple form of ax²+bx+c=0
2.) use the Quadratic equation formula to find the 2 SoluTions.
[tex] \large \green{ \bold{SOLUTION:}}[/tex]
[tex] \bold{4x {}^{2} - 4x + 1 = 7} \\ \bold{4x {}^{2} - 4x + 1 - 7= 0} \\ \bold{4x {}^{2} - 4x - 6 = 0} \\ \bold{ \cancel{ 4 \times} x {}^{2} - \cancel{ 4x }- \cancel{ 6} = 0} \\ \bold{2 \times x {}^{2} - 2x - 3 = 0} \\ \dashrightarrow \bold{a = 2 ,\: b = - 2 \: ,c = - 3}[/tex]
[tex] \large \green{ \bold{FORMULA:}}[/tex]
[tex] \large \bold{x_1,_2 = \frac{ - b \pm \sqrt{b {}^{2} - 4ac } }{2a} }[/tex]
[tex] \large \green{ \bold{SOLUTION:}}[/tex]
[tex] \bold{x_1,_2 = \frac{2 \pm \sqrt{( - 2) {}^{2} - 4 \times 2( - 3)} }{2 \times 2} }[/tex]
[tex] \bold{x_1,_2 = \frac{2 \pm \sqrt{( - 2) {}^{2} + 24 } }{2 \times 2}} [/tex]
[tex] \bold{x_1,_2 = \frac{2 \pm \sqrt{( - 2) {}^{2} + 24} }{2 \times 2} }[/tex]
[tex] \bold{x_1,_2 = \frac{2 \pm \sqrt{4 + 24} }{2 \times 2} }[/tex]
[tex] \bold{x_1,_2 = \frac{2 \pm \sqrt{28} }{2 \times 2} }[/tex]
[tex] \bold{x_1,_2 = \frac{2 \pm5.292}{2 \times 2} }[/tex]
[tex] \large \green{ \bold{FIRST \:SOLUTION:}}[/tex]
[tex] \bold{x_1 = \frac{2 + 5.292}{2 \times 2} }[/tex]
[tex] \bold{x_1 = \frac{2 + 5.292}{2 \times 2} }[/tex]
[tex] \bold{x_1 = \frac{2 + 5.292}{4}} [/tex]
[tex] \bold{x_1 = \frac{7.292}{4} }[/tex]
[tex]\large \bold»\color{darkviolet} \: \bold{x_1 = 1.823}[/tex]
[tex] \large \green{ \bold{SECOND\: SOLUTION :}}[/tex]
[tex] \bold{x_2 = \frac{2 - 5.292}{2 \times 2} }[/tex]
[tex] \bold{x_2 = \frac{2 - 5.292}{4} }[/tex]
[tex] \bold{x_2 = \frac{ - 3.292}{4}} [/tex]
[tex]\large\bold»\color{darkviolet} \: \bold{x_2 = - 0.823}[/tex]
[tex] \large \color{indigo}{ \bold{Carry\:On\: Latex}}[/tex]
