2 x 2 + 9 x + 10 ⇒ a = 2 b = 9 c = 10 ⇒ a c = 20 20 = 2 ∗ 10 = 4 ∗ 5 9 = 4 + 5 {\displaystyle {\begin{alignedat}{2}2x^{2}+9x+10\Rightarrow &a=2\\&b=9\\&c=10\\\end{alignedat}}\Rightarrow {\begin{alignedat}{2}&ac=20\\&{\begin{alignedat}{2}20&=2*10\\&=4*5\\\end{alignedat}}\\&9=4+5\\\end{alignedat}}}
2 x 2 + 9 x + 10 = 2 x 2 + 4 x + 5 x + 10 = 2 x ( x + 2 ) + 5 ( x + 2 ) = ( x + 2 ) ( 2 x + 5 ) {\displaystyle {\begin{alignedat}{2}2x^{2}+9x+10&=2x^{2}+4x+5x+10\\&=2x(x+2)+5(x+2)\\&=(x+2)(2x+5)\\\end{alignedat}}} ( x + 2 ) ( 2 x + 5 ) = 0 ⇒ x 1 = − 2 x 2 = − 5 / 2 {\displaystyle {\begin{alignedat}{2}(x+2)(2x+5)=0\Rightarrow &x_{1}=-2\\&x_{2}=-5/2\\\end{alignedat}}}
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2 x 2 + 9 x + 10 = 0 ⇒ {\displaystyle 2x^{2}+9x+10=0\Rightarrow } x 1 / 2 = − 9 ± 81 − 80 4 = − 9 ± 1 4 = − 9 ± 1 4 ⇒ x 1 = − 9 + 1 4 = − 2 x 2 = − 9 − 1 4 = − 5 2 {\displaystyle x_{1/2}={\frac {-9\pm {\sqrt {81-80}}}{4}}={\frac {-9\pm {\sqrt {1}}}{4}}={\frac {-9\pm 1}{4}}\Rightarrow {\begin{alignedat}{2}&x_{1}={\frac {-9+1}{4}}=-2\\&x_{2}={\frac {-9-1}{4}}=-{\frac {5}{2}}\\\end{alignedat}}} [1]
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