quadratic equation by completing the square 3x²-4x-4=0
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quadratic equation by completing the square 3x²-4x-4=0
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Answer:
[tex]x_{1} = - \frac{2}{3} \\ x_{2} = 2[/tex]
Step-by-step explanation:
[tex]3 {x}^{2} - 4x - 4 = 0[/tex]
Move the constant to the right-hand side and change its sign.
[tex]3 {x}^{2} - 4x = 4[/tex]
Divide both sides.
[tex] {x}^{2} - \frac{4}{3}x \: = \frac{4}{3} [/tex]
Add the same value to both sides.
[tex] {x}^{2} - \frac{4}{3}x \: +? \frac{4}{3} + ?[/tex]
add to the right hand side.
[tex] {x}^{2} - \frac{4}{3}x + \frac{4}{9} = \frac{4}{3} + \frac{4}{9} [/tex]
rewrite calculate the sum.
[tex](x - \frac{2}{3} )^{2} = \frac{16}{9} [/tex]
solve the equation=
[tex]x = - \frac{2}{3} \\ x = 2[/tex]
The equation has 2 solutions.
[tex]x_{1} = - \frac{2}{3} \: \: x_{2} = 2[/tex]