17=1+(x-1)*(x-1) eching

$$17=1+(x-1) \times (x-1)$$

x uchun yechish

$$x=5$$

$$x=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(x-1\right)^{2} hosil qilish uchun x-1 va x-1 ni ko'paytirish.

$$17=1+\left(x-1\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-1\right)^{2} kengaytirilishi uchun ishlating.

$$17=1+x^{2}-2x+1$$

2 olish uchun 1 va 1'ni qo'shing.

$$17=2+x^{2}-2x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2+x^{2}-2x=17$$

Ikkala tarafdan 17 ni ayirish.

$$2+x^{2}-2x-17=0$$

-15 olish uchun 2 dan 17 ni ayirish.

$$-15+x^{2}-2x=0$$

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.

$$x^{2}-2x-15=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -2 ni b va -15 ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-15\right)}}{2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-15\right)}}{2}$$

-4 ni -15 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+60}}{2}$$

4 ni 60 ga qo'shish.

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

64 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±8}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±8}{2}$$

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

$$x=\frac{10}{2}$$

10 ni 2 ga bo'lish.

$$x=5$$

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

$$x=-\frac{6}{2}$$

-6 ni 2 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=5 x=-3$$

Kvadratni yakunlash bo'yicha qadamlar

\left(x-1\right)^{2} hosil qilish uchun x-1 va x-1 ni ko'paytirish.

$$17=1+\left(x-1\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-1\right)^{2} kengaytirilishi uchun ishlating.

$$17=1+x^{2}-2x+1$$

2 olish uchun 1 va 1'ni qo'shing.

$$17=2+x^{2}-2x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2+x^{2}-2x=17$$

Ikkala tarafdan 2 ni ayirish.

$$x^{2}-2x=17-2$$

15 olish uchun 17 dan 2 ni ayirish.

$$x^{2}-2x=15$$

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-2x+1=15+1$$

15 ni 1 ga qo'shish.

$$x^{2}-2x+1=16$$

x^{2}-2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-1\right)^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{16}$$

Qisqartirish.

$$x-1=4 x-1=-4$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=5 x=-3$$