6(135)={left(x-2*1/2right)}^2 eching

$$6(135)= { \left(x-2 \times \frac{ 1 }{ 2 } \right) }^{ 2 }$$

x uchun yechish

$$x=9\sqrt{10}+1\approx 29,460498942$$

$$x=1-9\sqrt{10}\approx -27,460498942$$

Kvadrat tenglamalaridan foydalanish qoidalari

810 hosil qilish uchun 6 va 135 ni ko'paytirish.

$$810=\left(x-2\times \frac{1}{2}\right)^{2}$$

1 hosil qilish uchun 2 va \frac{1}{2} ni ko'paytirish.

$$810=\left(x-1\right)^{2}$$

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

$$810=x^{2}-2x+1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-2x+1=810$$

Ikkala tarafdan 810 ni ayirish.

$$x^{2}-2x+1-810=0$$

-809 olish uchun 1 dan 810 ni ayirish.

$$x^{2}-2x-809=0$$

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 -809 ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-809\right)}}{2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-809\right)}}{2}$$

-4 ni -809 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+3236}}{2}$$

4 ni 3236 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{3240}}{2}$$

3240 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±18\sqrt{10}}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±18\sqrt{10}}{2}$$

x=\frac{2±18\sqrt{10}}{2} tenglamasini yeching, bunda ± musbat. 2 ni 18\sqrt{10} ga qo'shish.

$$x=\frac{18\sqrt{10}+2}{2}$$

2+18\sqrt{10} ni 2 ga bo'lish.

$$x=9\sqrt{10}+1$$

x=\frac{2±18\sqrt{10}}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 18\sqrt{10} ni ayirish.

$$x=\frac{2-18\sqrt{10}}{2}$$

2-18\sqrt{10} ni 2 ga bo'lish.

$$x=1-9\sqrt{10}$$

Tenglama yechildi.

$$x=9\sqrt{10}+1 x=1-9\sqrt{10}$$

Kvadratni yakunlash bo'yicha qadamlar

810 hosil qilish uchun 6 va 135 ni ko'paytirish.

$$810=\left(x-2\times \frac{1}{2}\right)^{2}$$

1 hosil qilish uchun 2 va \frac{1}{2} ni ko'paytirish.

$$810=\left(x-1\right)^{2}$$

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

$$810=x^{2}-2x+1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-2x+1=810$$

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.

$$\left(x-1\right)^{2}=810$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{810}$$

Qisqartirish.

$$x-1=9\sqrt{10} x-1=-9\sqrt{10}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=9\sqrt{10}+1 x=1-9\sqrt{10}$$