Issolvi left(x-2right)^2+left(x-1right)^2+x^2=left(x+1right)^2+{left(x+2right)}^2

$${ \left(x-2 \right) }^{ 2 } + { \left(x-1 \right) }^{ 2 } + { x }^{ 2 } = { \left(x+1 \right) }^{ 2 } + { \left(x+2 \right) }^{ 2 }$$

Solvi għal x

$$x=12$$

$$x=0$$

Passi li jużaw il-Fatturar

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-2\right)^{2}.

$$x^{2}-4x+4+\left(x-1\right)^{2}+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-1\right)^{2}.

$$x^{2}-4x+4+x^{2}-2x+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Ikkombina x^{2} u x^{2} biex tikseb 2x^{2}.

$$2x^{2}-4x+4-2x+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Ikkombina -4x u -2x biex tikseb -6x.

$$2x^{2}-6x+4+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Żid 4 u 1 biex tikseb 5.

$$2x^{2}-6x+5+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Ikkombina 2x^{2} u x^{2} biex tikseb 3x^{2}.

$$3x^{2}-6x+5=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+1\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+\left(x+2\right)^{2}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+2\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+x^{2}+4x+4$$

Ikkombina x^{2} u x^{2} biex tikseb 2x^{2}.

$$3x^{2}-6x+5=2x^{2}+2x+1+4x+4$$

Ikkombina 2x u 4x biex tikseb 6x.

$$3x^{2}-6x+5=2x^{2}+6x+1+4$$

Żid 1 u 4 biex tikseb 5.

$$3x^{2}-6x+5=2x^{2}+6x+5$$

Naqqas 2x^{2} miż-żewġ naħat.

$$3x^{2}-6x+5-2x^{2}=6x+5$$

Ikkombina 3x^{2} u -2x^{2} biex tikseb x^{2}.

$$x^{2}-6x+5=6x+5$$

Naqqas 6x miż-żewġ naħat.

$$x^{2}-6x+5-6x=5$$

Ikkombina -6x u -6x biex tikseb -12x.

$$x^{2}-12x+5=5$$

Naqqas 5 miż-żewġ naħat.

$$x^{2}-12x+5-5=0$$

Naqqas 5 minn 5 biex tikseb 0.

$$x^{2}-12x=0$$

Iffattura 'l barra x.

$$x\left(x-12\right)=0$$

Biex issib soluzzjonijiet tal-ekwazzjoni, solvi x=0 u x-12=0.

$$x=0 x=12$$

Passi għall-Użu tal-Formula Kwadratika

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-2\right)^{2}.

$$x^{2}-4x+4+\left(x-1\right)^{2}+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-1\right)^{2}.

$$x^{2}-4x+4+x^{2}-2x+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Ikkombina x^{2} u x^{2} biex tikseb 2x^{2}.

$$2x^{2}-4x+4-2x+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Ikkombina -4x u -2x biex tikseb -6x.

$$2x^{2}-6x+4+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Żid 4 u 1 biex tikseb 5.

$$2x^{2}-6x+5+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Ikkombina 2x^{2} u x^{2} biex tikseb 3x^{2}.

$$3x^{2}-6x+5=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+1\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+\left(x+2\right)^{2}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+2\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+x^{2}+4x+4$$

Ikkombina x^{2} u x^{2} biex tikseb 2x^{2}.

$$3x^{2}-6x+5=2x^{2}+2x+1+4x+4$$

Ikkombina 2x u 4x biex tikseb 6x.

$$3x^{2}-6x+5=2x^{2}+6x+1+4$$

Żid 1 u 4 biex tikseb 5.

$$3x^{2}-6x+5=2x^{2}+6x+5$$

Naqqas 2x^{2} miż-żewġ naħat.

$$3x^{2}-6x+5-2x^{2}=6x+5$$

Ikkombina 3x^{2} u -2x^{2} biex tikseb x^{2}.

$$x^{2}-6x+5=6x+5$$

Naqqas 6x miż-żewġ naħat.

$$x^{2}-6x+5-6x=5$$

Ikkombina -6x u -6x biex tikseb -12x.

$$x^{2}-12x+5=5$$

Naqqas 5 miż-żewġ naħat.

$$x^{2}-12x+5-5=0$$

Naqqas 5 minn 5 biex tikseb 0.

$$x^{2}-12x=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 1 għal a, -12 għal b, u 0 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2}$$

Ħu l-għerq kwadrat ta' \left(-12\right)^{2}.

$$x=\frac{-\left(-12\right)±12}{2}$$

L-oppost ta' -12 huwa 12.

$$x=\frac{12±12}{2}$$

Issa solvi l-ekwazzjoni x=\frac{12±12}{2} fejn ± hija plus. Żid 12 ma' 12.

$$x=\frac{24}{2}$$

Iddividi 24 b'2.

$$x=12$$

Issa solvi l-ekwazzjoni x=\frac{12±12}{2} fejn ± hija minus. Naqqas 12 minn 12.

$$x=\frac{0}{2}$$

Iddividi 0 b'2.

$$x=0$$

L-ekwazzjoni issa solvuta.

$$x=12 x=0$$

Passi biex Tikkompleta l-Kwadrat

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-2\right)^{2}.

$$x^{2}-4x+4+\left(x-1\right)^{2}+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-1\right)^{2}.

$$x^{2}-4x+4+x^{2}-2x+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Ikkombina x^{2} u x^{2} biex tikseb 2x^{2}.

$$2x^{2}-4x+4-2x+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Ikkombina -4x u -2x biex tikseb -6x.

$$2x^{2}-6x+4+1+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Żid 4 u 1 biex tikseb 5.

$$2x^{2}-6x+5+x^{2}=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Ikkombina 2x^{2} u x^{2} biex tikseb 3x^{2}.

$$3x^{2}-6x+5=\left(x+1\right)^{2}+\left(x+2\right)^{2}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+1\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+\left(x+2\right)^{2}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+2\right)^{2}.

$$3x^{2}-6x+5=x^{2}+2x+1+x^{2}+4x+4$$

Ikkombina x^{2} u x^{2} biex tikseb 2x^{2}.

$$3x^{2}-6x+5=2x^{2}+2x+1+4x+4$$

Ikkombina 2x u 4x biex tikseb 6x.

$$3x^{2}-6x+5=2x^{2}+6x+1+4$$

Żid 1 u 4 biex tikseb 5.

$$3x^{2}-6x+5=2x^{2}+6x+5$$

Naqqas 2x^{2} miż-żewġ naħat.

$$3x^{2}-6x+5-2x^{2}=6x+5$$

Ikkombina 3x^{2} u -2x^{2} biex tikseb x^{2}.

$$x^{2}-6x+5=6x+5$$

Naqqas 6x miż-żewġ naħat.

$$x^{2}-6x+5-6x=5$$

Ikkombina -6x u -6x biex tikseb -12x.

$$x^{2}-12x+5=5$$

Naqqas 5 miż-żewġ naħat.

$$x^{2}-12x+5-5=0$$

Naqqas 5 minn 5 biex tikseb 0.

$$x^{2}-12x=0$$

Iddividi -12, il-koeffiċjent tat-terminu x, b'2 biex tikseb -6. Imbagħad żid il-kwadru ta' -6 maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}-12x+\left(-6\right)^{2}=\left(-6\right)^{2}$$

Ikkwadra -6.

$$x^{2}-12x+36=36$$

Fattur x^{2}-12x+36. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-6\right)^{2}=36$$

Ħu l-għerq kwadrat taż-żewġ naħat tal-ekwazzjoni.

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{36}$$

Issimplifika.

$$x-6=6 x-6=-6$$

Żid 6 maż-żewġ naħat tal-ekwazzjoni.

$$x=12 x=0$$