Issolvi x+2/4-[2(1-x)]^2/64=-(x+1/4)^2+(1-1/2)x+frac{1}{2}

$$\frac { x + 2 } { 4 } - \frac { [ 2 ( 1 - x ) ] ^ { 2 } } { 64 } = - ( \frac { x + 1 } { 4 } ) ^ { 2 } + ( 1 - \frac { 1 } { 2 } ) x + \frac { 1 } { 2 }$$

Solvi għal x (complex solution)

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

Passi Qosra tas-Soluzzjonijiet

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'64, l-inqas denominatur komuni ta' 4,64,2.

$$16\left(x+2\right)-\left(2\left(1-x\right)\right)^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Uża l-propjetà distributtiva biex timmultiplika 16 b'x+2.

$$16x+32-\left(2\left(1-x\right)\right)^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'1-x.

$$16x+32-\left(2-2x\right)^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

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

$$16x+32-\left(4-8x+4x^{2}\right)=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Biex issib l-oppost ta' 4-8x+4x^{2}, sib l-oppost ta' kull terminu.

$$16x+32-4+8x-4x^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Naqqas 4 minn 32 biex tikseb 28.

$$16x+28+8x-4x^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Ikkombina 16x u 8x biex tikseb 24x.

$$24x+28-4x^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Biex tgħolli \frac{x+1}{4} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$24x+28-4x^{2}=-64\times \frac{\left(x+1\right)^{2}}{4^{2}}+64\left(1-\frac{1}{2}\right)x+32$$

Esprimi -64\times \frac{\left(x+1\right)^{2}}{4^{2}} bħala frazzjoni waħda.

$$24x+28-4x^{2}=\frac{-64\left(x+1\right)^{2}}{4^{2}}+64\left(1-\frac{1}{2}\right)x+32$$

Naqqas \frac{1}{2} minn 1 biex tikseb \frac{1}{2}.

$$24x+28-4x^{2}=\frac{-64\left(x+1\right)^{2}}{4^{2}}+64\times \frac{1}{2}x+32$$

Immultiplika 64 u \frac{1}{2} biex tikseb 32.

$$24x+28-4x^{2}=\frac{-64\left(x+1\right)^{2}}{4^{2}}+32x+32$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 32x+32 b'\frac{4^{2}}{4^{2}}.

$$24x+28-4x^{2}=\frac{-64\left(x+1\right)^{2}}{4^{2}}+\frac{\left(32x+32\right)\times 4^{2}}{4^{2}}$$

Billi \frac{-64\left(x+1\right)^{2}}{4^{2}} u \frac{\left(32x+32\right)\times 4^{2}}{4^{2}} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$24x+28-4x^{2}=\frac{-64\left(x+1\right)^{2}+\left(32x+32\right)\times 4^{2}}{4^{2}}$$

Agħmel il-multiplikazzjonijiet fi -64\left(x+1\right)^{2}+\left(32x+32\right)\times 4^{2}.

$$24x+28-4x^{2}=\frac{-64x^{2}-128x-64+512x+512}{4^{2}}$$

Ikkombina termini simili f'-64x^{2}-128x-64+512x+512.

$$24x+28-4x^{2}=\frac{-64x^{2}+384x+448}{4^{2}}$$

Ikkalkula 4 bil-power ta' 2 u tikseb 16.

$$24x+28-4x^{2}=\frac{-64x^{2}+384x+448}{16}$$

Iddividi kull terminu ta' -64x^{2}+384x+448 b'16 biex tikseb-4x^{2}+24x+28.

$$24x+28-4x^{2}=-4x^{2}+24x+28$$

Żid 4x^{2} maż-żewġ naħat.

$$24x+28-4x^{2}+4x^{2}=24x+28$$

Ikkombina -4x^{2} u 4x^{2} biex tikseb 0.

$$24x+28=24x+28$$

Naqqas 24x miż-żewġ naħat.

$$24x+28-24x=28$$

Ikkombina 24x u -24x biex tikseb 0.

$$28=28$$

Qabbel 28 u 28.

$$\text{true}$$

Din hija vera għal kwalunkwe x.

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

Solvi għal x

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

Passi Qosra tas-Soluzzjonijiet

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'64, l-inqas denominatur komuni ta' 4,64,2.

$$16\left(x+2\right)-\left(2\left(1-x\right)\right)^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Uża l-propjetà distributtiva biex timmultiplika 16 b'x+2.

$$16x+32-\left(2\left(1-x\right)\right)^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'1-x.

$$16x+32-\left(2-2x\right)^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

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

$$16x+32-\left(4-8x+4x^{2}\right)=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Biex issib l-oppost ta' 4-8x+4x^{2}, sib l-oppost ta' kull terminu.

$$16x+32-4+8x-4x^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Naqqas 4 minn 32 biex tikseb 28.

$$16x+28+8x-4x^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Ikkombina 16x u 8x biex tikseb 24x.

$$24x+28-4x^{2}=-64\times \left(\frac{x+1}{4}\right)^{2}+64\left(1-\frac{1}{2}\right)x+32$$

Biex tgħolli \frac{x+1}{4} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

$$24x+28-4x^{2}=-64\times \frac{\left(x+1\right)^{2}}{4^{2}}+64\left(1-\frac{1}{2}\right)x+32$$

Esprimi -64\times \frac{\left(x+1\right)^{2}}{4^{2}} bħala frazzjoni waħda.

$$24x+28-4x^{2}=\frac{-64\left(x+1\right)^{2}}{4^{2}}+64\left(1-\frac{1}{2}\right)x+32$$

Naqqas \frac{1}{2} minn 1 biex tikseb \frac{1}{2}.

$$24x+28-4x^{2}=\frac{-64\left(x+1\right)^{2}}{4^{2}}+64\times \frac{1}{2}x+32$$

Immultiplika 64 u \frac{1}{2} biex tikseb 32.

$$24x+28-4x^{2}=\frac{-64\left(x+1\right)^{2}}{4^{2}}+32x+32$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 32x+32 b'\frac{4^{2}}{4^{2}}.

$$24x+28-4x^{2}=\frac{-64\left(x+1\right)^{2}}{4^{2}}+\frac{\left(32x+32\right)\times 4^{2}}{4^{2}}$$

Billi \frac{-64\left(x+1\right)^{2}}{4^{2}} u \frac{\left(32x+32\right)\times 4^{2}}{4^{2}} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$24x+28-4x^{2}=\frac{-64\left(x+1\right)^{2}+\left(32x+32\right)\times 4^{2}}{4^{2}}$$

Agħmel il-multiplikazzjonijiet fi -64\left(x+1\right)^{2}+\left(32x+32\right)\times 4^{2}.

$$24x+28-4x^{2}=\frac{-64x^{2}-128x-64+512x+512}{4^{2}}$$

Ikkombina termini simili f'-64x^{2}-128x-64+512x+512.

$$24x+28-4x^{2}=\frac{-64x^{2}+384x+448}{4^{2}}$$

Ikkalkula 4 bil-power ta' 2 u tikseb 16.

$$24x+28-4x^{2}=\frac{-64x^{2}+384x+448}{16}$$

Iddividi kull terminu ta' -64x^{2}+384x+448 b'16 biex tikseb-4x^{2}+24x+28.

$$24x+28-4x^{2}=-4x^{2}+24x+28$$

Żid 4x^{2} maż-żewġ naħat.

$$24x+28-4x^{2}+4x^{2}=24x+28$$

Ikkombina -4x^{2} u 4x^{2} biex tikseb 0.

$$24x+28=24x+28$$

Naqqas 24x miż-żewġ naħat.

$$24x+28-24x=28$$

Ikkombina 24x u -24x biex tikseb 0.

$$28=28$$

Qabbel 28 u 28.

$$\text{true}$$

Din hija vera għal kwalunkwe x.

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