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SCORPION-xisa [38]
4 years ago
15

Simplify all radicals as far as you can. 9x2 + 12x +4= 0

Mathematics
1 answer:
RoseWind [281]4 years ago
7 0

Note that 9x^2 + 12x +4= 0 has the form of a special product:

(a + b)^2 = a^2 + 2ab + b^2

and so our 9x^2 + 12x +4= 0 factors into (3x + 2)(3x + 2) = (3x + 2)^2

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zavuch27 [327]
1^{o} \\  \\ 4x^{2}-9=0 \\  \\ (2x-3)(2x+3)=0 \\  \\ 2x-3=0 \ \vee \ 2x+3=0 \\  \\ 2x=3 \ \vee \ 2x=-3 \\  \\ x= \frac{3}{2}  \ \vee \ x=- \frac{3}{2}  \\  \\ 2^{o} \\  \\ 4x^{2}-9=0 \\  \\ 4x^{2}=9 \\  \\ x^{2}= \frac{9}{4}  \\  \\ x= \sqrt{ \frac{9}{4} } \ \vee \ -\sqrt{ \frac{9}{4} }  \\  \\ x= \frac{3}{2} \ \vee \ x=- \frac{3}{2}  \\  \\ 3^{o} \\  \\ 4x^{2}-9=0 \\  \\ \Delta=0^{2}-4*4*(-9)=144 \\  \\  \sqrt{\Delta}  =12 \\  \\ x_{1}= \frac{0+12}{8} = \frac{3}{2}

x_{2}= \frac{0-12}{8} =- \frac{3}{2}
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