Issolvi 3x(x+1)-(x-2)^2-6=(x+3)(x-5)+x*(x+9)+5

$$3 x ( x + 1 ) - ( x - 2 ) ^ { 2 } - 6 = ( x + 3 ) ( x - 5 ) + x \cdot ( x + 9 ) + 5$$

Solvi għal x (complex solution)

$$x\in \mathrm{C}$$

Passi tas-Soluzzjonijiet

Uża l-propjetà distributtiva biex timmultiplika 3x b'x+1.

$$3x^{2}+3x-\left(x-2\right)^{2}-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

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

$$3x^{2}+3x-\left(x^{2}-4x+4\right)-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Biex issib l-oppost ta' x^{2}-4x+4, sib l-oppost ta' kull terminu.

$$3x^{2}+3x-x^{2}+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

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

$$2x^{2}+3x+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Ikkombina 3x u 4x biex tikseb 7x.

$$2x^{2}+7x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Naqqas 6 minn -4 biex tikseb -10.

$$2x^{2}+7x-10=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Uża l-propjetà distributtiva biex timmultiplika x+3 b'x-5 u kkombina termini simili.

$$2x^{2}+7x-10=x^{2}-2x-15+x\left(x+9\right)+5$$

Uża l-propjetà distributtiva biex timmultiplika x b'x+9.

$$2x^{2}+7x-10=x^{2}-2x-15+x^{2}+9x+5$$

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

$$2x^{2}+7x-10=2x^{2}-2x-15+9x+5$$

Ikkombina -2x u 9x biex tikseb 7x.

$$2x^{2}+7x-10=2x^{2}+7x-15+5$$

Żid -15 u 5 biex tikseb -10.

$$2x^{2}+7x-10=2x^{2}+7x-10$$

Naqqas 2x^{2} miż-żewġ naħat.

$$2x^{2}+7x-10-2x^{2}=7x-10$$

Ikkombina 2x^{2} u -2x^{2} biex tikseb 0.

$$7x-10=7x-10$$

Naqqas 7x miż-żewġ naħat.

$$7x-10-7x=-10$$

Ikkombina 7x u -7x biex tikseb 0.

$$-10=-10$$

Qabbel -10 u -10.

$$\text{true}$$

Din hija vera għal kwalunkwe x.

$$x\in \mathrm{C}$$

Solvi għal x

$$x\in \mathrm{R}$$

Passi tas-Soluzzjonijiet

Uża l-propjetà distributtiva biex timmultiplika 3x b'x+1.

$$3x^{2}+3x-\left(x-2\right)^{2}-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

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

$$3x^{2}+3x-\left(x^{2}-4x+4\right)-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Biex issib l-oppost ta' x^{2}-4x+4, sib l-oppost ta' kull terminu.

$$3x^{2}+3x-x^{2}+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

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

$$2x^{2}+3x+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Ikkombina 3x u 4x biex tikseb 7x.

$$2x^{2}+7x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Naqqas 6 minn -4 biex tikseb -10.

$$2x^{2}+7x-10=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Uża l-propjetà distributtiva biex timmultiplika x+3 b'x-5 u kkombina termini simili.

$$2x^{2}+7x-10=x^{2}-2x-15+x\left(x+9\right)+5$$

Uża l-propjetà distributtiva biex timmultiplika x b'x+9.

$$2x^{2}+7x-10=x^{2}-2x-15+x^{2}+9x+5$$

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

$$2x^{2}+7x-10=2x^{2}-2x-15+9x+5$$

Ikkombina -2x u 9x biex tikseb 7x.

$$2x^{2}+7x-10=2x^{2}+7x-15+5$$

Żid -15 u 5 biex tikseb -10.

$$2x^{2}+7x-10=2x^{2}+7x-10$$

Naqqas 2x^{2} miż-żewġ naħat.

$$2x^{2}+7x-10-2x^{2}=7x-10$$

Ikkombina 2x^{2} u -2x^{2} biex tikseb 0.

$$7x-10=7x-10$$

Naqqas 7x miż-żewġ naħat.

$$7x-10-7x=-10$$

Ikkombina 7x u -7x biex tikseb 0.

$$-10=-10$$

Qabbel -10 u -10.

$$\text{true}$$

Din hija vera għal kwalunkwe x.

$$x\in \mathrm{R}$$