Issolvi (-4x-2)^2+(2-4x)^2=50

$$( - 4 x - 2 ) ^ { 2 } + ( 2 - 4 x ) ^ { 2 } = 50$$

Solvi għal x

$$x = -\frac{\sqrt{21}}{4} \approx -1.145643924$$

$$x = \frac{\sqrt{21}}{4} \approx 1.145643924$$

Passi billi Ssib l-Għerq Kwadrat

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(-4x-2\right)^{2}.

$$16x^{2}+16x+4+\left(2-4x\right)^{2}=50$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(2-4x\right)^{2}.

$$16x^{2}+16x+4+4-16x+16x^{2}=50$$

Żid 4 u 4 biex tikseb 8.

$$16x^{2}+16x+8-16x+16x^{2}=50$$

Ikkombina 16x u -16x biex tikseb 0.

$$16x^{2}+8+16x^{2}=50$$

Ikkombina 16x^{2} u 16x^{2} biex tikseb 32x^{2}.

$$32x^{2}+8=50$$

Naqqas 8 miż-żewġ naħat.

$$32x^{2}=50-8$$

Naqqas 8 minn 50 biex tikseb 42.

$$32x^{2}=42$$

Iddividi ż-żewġ naħat b'32.

$$x^{2}=\frac{42}{32}$$

Naqqas il-frazzjoni \frac{42}{32} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$x^{2}=\frac{21}{16}$$

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

$$x=\frac{\sqrt{21}}{4} x=-\frac{\sqrt{21}}{4}$$

Passi għall-Użu tal-Formula Kwadratika

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(-4x-2\right)^{2}.

$$16x^{2}+16x+4+\left(2-4x\right)^{2}=50$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(2-4x\right)^{2}.

$$16x^{2}+16x+4+4-16x+16x^{2}=50$$

Żid 4 u 4 biex tikseb 8.

$$16x^{2}+16x+8-16x+16x^{2}=50$$

Ikkombina 16x u -16x biex tikseb 0.

$$16x^{2}+8+16x^{2}=50$$

Ikkombina 16x^{2} u 16x^{2} biex tikseb 32x^{2}.

$$32x^{2}+8=50$$

Naqqas 50 miż-żewġ naħat.

$$32x^{2}+8-50=0$$

Naqqas 50 minn 8 biex tikseb -42.

$$32x^{2}-42=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 32 għal a, 0 għal b, u -42 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 32\left(-42\right)}}{2\times 32}$$

Ikkwadra 0.

$$x=\frac{0±\sqrt{-4\times 32\left(-42\right)}}{2\times 32}$$

Immultiplika -4 b'32.

$$x=\frac{0±\sqrt{-128\left(-42\right)}}{2\times 32}$$

Immultiplika -128 b'-42.

$$x=\frac{0±\sqrt{5376}}{2\times 32}$$

Ħu l-għerq kwadrat ta' 5376.

$$x=\frac{0±16\sqrt{21}}{2\times 32}$$

Immultiplika 2 b'32.

$$x=\frac{0±16\sqrt{21}}{64}$$

Issa solvi l-ekwazzjoni x=\frac{0±16\sqrt{21}}{64} fejn ± hija plus.

$$x=\frac{\sqrt{21}}{4}$$

Issa solvi l-ekwazzjoni x=\frac{0±16\sqrt{21}}{64} fejn ± hija minus.

$$x=-\frac{\sqrt{21}}{4}$$

L-ekwazzjoni issa solvuta.

$$x=\frac{\sqrt{21}}{4} x=-\frac{\sqrt{21}}{4}$$