Issolvi (11n^2+2n-8)+(4n^2-5n+7)

$$( 11 n ^ { 2 } + 2 n - 8 ) + ( 4 n ^ { 2 } - 5 n + 7 )$$

Evalwa

$$15n^{2}-3n-1$$

Passi tas-Soluzzjonijiet

Ikkombina 11n^{2} u 4n^{2} biex tikseb 15n^{2}.

$$15n^{2}+2n-8-5n+7$$

Ikkombina 2n u -5n biex tikseb -3n.

$$15n^{2}-3n-8+7$$

Żid -8 u 7 biex tikseb -1.

$$15n^{2}-3n-1$$

Fattur

$$15\left(n-\left(-\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)\left(n-\left(\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)$$

Passi għall-Użu tal-Formula Kwadratika

Ikkombina 11n^{2} u 4n^{2} biex tikseb 15n^{2}.

$$factor(15n^{2}+2n-8-5n+7)$$

Ikkombina 2n u -5n biex tikseb -3n.

$$factor(15n^{2}-3n-8+7)$$

Żid -8 u 7 biex tikseb -1.

$$factor(15n^{2}-3n-1)$$

Polynomial kwadratika tista' tiġi fatturata billi tuża t-trasformazzjoni ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), fejn x_{1} u x_{2} huma s-soluzzjonijiet tal-ekwazzjoni kwadratika ax^{2}+bx+c=0.

$$15n^{2}-3n-1=0$$

L-ekwazzjonijiet kollha tal-formola ax^{2}+bx+c=0 jistgħu jiġu solvuti permezz tal-formula kwadratika: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Il-formula kwadratika tagħti żewġ soluzzjonijiet, waħda meta ± hija addizzjoni u waħda meta hija tnaqqis.

$$n=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 15\left(-1\right)}}{2\times 15}$$

Ikkwadra -3.

$$n=\frac{-\left(-3\right)±\sqrt{9-4\times 15\left(-1\right)}}{2\times 15}$$

Immultiplika -4 b'15.

$$n=\frac{-\left(-3\right)±\sqrt{9-60\left(-1\right)}}{2\times 15}$$

Immultiplika -60 b'-1.

$$n=\frac{-\left(-3\right)±\sqrt{9+60}}{2\times 15}$$

Żid 9 ma' 60.

$$n=\frac{-\left(-3\right)±\sqrt{69}}{2\times 15}$$

L-oppost ta' -3 huwa 3.

$$n=\frac{3±\sqrt{69}}{2\times 15}$$

Immultiplika 2 b'15.

$$n=\frac{3±\sqrt{69}}{30}$$

Issa solvi l-ekwazzjoni n=\frac{3±\sqrt{69}}{30} fejn ± hija plus. Żid 3 ma' \sqrt{69}.

$$n=\frac{\sqrt{69}+3}{30}$$

Iddividi 3+\sqrt{69} b'30.

$$n=\frac{\sqrt{69}}{30}+\frac{1}{10}$$

Issa solvi l-ekwazzjoni n=\frac{3±\sqrt{69}}{30} fejn ± hija minus. Naqqas \sqrt{69} minn 3.

$$n=\frac{3-\sqrt{69}}{30}$$

Iddividi 3-\sqrt{69} b'30.

$$n=-\frac{\sqrt{69}}{30}+\frac{1}{10}$$

Iffattura l-espressjoni oriġinali permezz ta’ ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Issostitwixxi \frac{1}{10}+\frac{\sqrt{69}}{30} għal x_{1} u \frac{1}{10}-\frac{\sqrt{69}}{30} għal x_{2}.

$$15n^{2}-3n-1=15\left(n-\left(\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)\left(n-\left(-\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)$$