(x+6)-3*x+2=(x+6)*x eching

$$( x + 6 ) - 3 \cdot x + 2 = ( x + 6 ) \cdot x$$

x uchun yechish

$$x=2\sqrt{6}-4\approx 0,898979486$$

$$x=-2\sqrt{6}-4\approx -8,898979486$$

Kvadrat tenglamalaridan foydalanish qoidalari

-2x ni olish uchun x va -3x ni birlashtirish.

$$-2x+6+2=\left(x+6\right)x$$

8 olish uchun 6 va 2'ni qo'shing.

$$-2x+8=\left(x+6\right)x$$

x+6 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-2x+8=x^{2}+6x$$

Ikkala tarafdan x^{2} ni ayirish.

$$-2x+8-x^{2}=6x$$

Ikkala tarafdan 6x ni ayirish.

$$-2x+8-x^{2}-6x=0$$

-8x ni olish uchun -2x va -6x ni birlashtirish.

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

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -8 ni b va 8 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+4\times 8}}{2\left(-1\right)}$$

4 ni 8 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+32}}{2\left(-1\right)}$$

64 ni 32 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{96}}{2\left(-1\right)}$$

96 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±4\sqrt{6}}{2\left(-1\right)}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±4\sqrt{6}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{8±4\sqrt{6}}{-2}$$

x=\frac{8±4\sqrt{6}}{-2} tenglamasini yeching, bunda ± musbat. 8 ni 4\sqrt{6} ga qo'shish.

$$x=\frac{4\sqrt{6}+8}{-2}$$

8+4\sqrt{6} ni -2 ga bo'lish.

$$x=-2\sqrt{6}-4$$

x=\frac{8±4\sqrt{6}}{-2} tenglamasini yeching, bunda ± manfiy. 8 dan 4\sqrt{6} ni ayirish.

$$x=\frac{8-4\sqrt{6}}{-2}$$

8-4\sqrt{6} ni -2 ga bo'lish.

$$x=2\sqrt{6}-4$$

Tenglama yechildi.

$$x=-2\sqrt{6}-4 x=2\sqrt{6}-4$$

Kvadratni yakunlash bo'yicha qadamlar

-2x ni olish uchun x va -3x ni birlashtirish.

$$-2x+6+2=\left(x+6\right)x$$

8 olish uchun 6 va 2'ni qo'shing.

$$-2x+8=\left(x+6\right)x$$

x+6 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-2x+8=x^{2}+6x$$

Ikkala tarafdan x^{2} ni ayirish.

$$-2x+8-x^{2}=6x$$

Ikkala tarafdan 6x ni ayirish.

$$-2x+8-x^{2}-6x=0$$

-8x ni olish uchun -2x va -6x ni birlashtirish.

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

Ikkala tarafdan 8 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-8x}{-1}=-\frac{8}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{8}{-1}\right)x=-\frac{8}{-1}$$

-8 ni -1 ga bo'lish.

$$x^{2}+8x=-\frac{8}{-1}$$

-8 ni -1 ga bo'lish.

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

8 ni bo‘lish, x shartining koeffitsienti, 2 ga 4 olish uchun. Keyin, 4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+8x+4^{2}=8+4^{2}$$

4 kvadratini chiqarish.

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

8 ni 16 ga qo'shish.

$$x^{2}+8x+16=24$$

x^{2}+8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+4\right)^{2}=24$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{24}$$

Qisqartirish.

$$x+4=2\sqrt{6} x+4=-2\sqrt{6}$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=2\sqrt{6}-4 x=-2\sqrt{6}-4$$