(4-x)(4-x)=9 eching

$$(4-x)(4-x)=9$$

x uchun yechish

$$x=1$$

$$x=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(4-x\right)^{2} hosil qilish uchun 4-x va 4-x ni ko'paytirish.

$$\left(4-x\right)^{2}=9$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(4-x\right)^{2} kengaytirilishi uchun ishlating.

$$16-8x+x^{2}=9$$

Ikkala tarafdan 9 ni ayirish.

$$16-8x+x^{2}-9=0$$

7 olish uchun 16 dan 9 ni ayirish.

$$7-8x+x^{2}=0$$

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.

$$x^{2}-8x+7=0$$

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 7 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 7}}{2}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 7}}{2}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-28}}{2}$$

64 ni -28 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{36}}{2}$$

36 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±6}{2}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±6}{2}$$

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

$$x=\frac{14}{2}$$

14 ni 2 ga bo'lish.

$$x=7$$

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

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

2 ni 2 ga bo'lish.

$$x=1$$

Tenglama yechildi.

$$x=7 x=1$$

Kvadratni yakunlash bo'yicha qadamlar

\left(4-x\right)^{2} hosil qilish uchun 4-x va 4-x ni ko'paytirish.

$$\left(4-x\right)^{2}=9$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(4-x\right)^{2} kengaytirilishi uchun ishlating.

$$16-8x+x^{2}=9$$

Ikkala tarafdan 16 ni ayirish.

$$-8x+x^{2}=9-16$$

-7 olish uchun 9 dan 16 ni ayirish.

$$-8x+x^{2}=-7$$

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

$$x^{2}-8x=-7$$

-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.

$$x^{2}-8x+\left(-4\right)^{2}=-7+\left(-4\right)^{2}$$

-4 kvadratini chiqarish.

$$x^{2}-8x+16=-7+16$$

-7 ni 16 ga qo'shish.

$$x^{2}-8x+16=9$$

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.

$$\left(x-4\right)^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{9}$$

Qisqartirish.

$$x-4=3 x-4=-3$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$x=7 x=1$$