2x^2=18x-1 eching

$$2 { x }^{ 2 } =18x-1$$

x uchun yechish

$$x = \frac{\sqrt{79} + 9}{2} \approx 8,944097209$$

$$x=\frac{9-\sqrt{79}}{2}\approx 0,055902791$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 18x ni ayirish.

$$2x^{2}-18x=-1$$

1 ni ikki tarafga qo’shing.

$$2x^{2}-18x+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -18 ni b va 1 ni c bilan almashtiring.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 2}}{2\times 2}$$

-18 kvadratini chiqarish.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 2}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324-8}}{2\times 2}$$

324 ni -8 ga qo'shish.

$$x=\frac{-\left(-18\right)±\sqrt{316}}{2\times 2}$$

316 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±2\sqrt{79}}{2\times 2}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±2\sqrt{79}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{18±2\sqrt{79}}{4}$$

x=\frac{18±2\sqrt{79}}{4} tenglamasini yeching, bunda ± musbat. 18 ni 2\sqrt{79} ga qo'shish.

$$x=\frac{2\sqrt{79}+18}{4}$$

18+2\sqrt{79} ni 4 ga bo'lish.

$$x=\frac{\sqrt{79}+9}{2}$$

x=\frac{18±2\sqrt{79}}{4} tenglamasini yeching, bunda ± manfiy. 18 dan 2\sqrt{79} ni ayirish.

$$x=\frac{18-2\sqrt{79}}{4}$$

18-2\sqrt{79} ni 4 ga bo'lish.

$$x=\frac{9-\sqrt{79}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{79}+9}{2} x=\frac{9-\sqrt{79}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 18x ni ayirish.

$$2x^{2}-18x=-1$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-18x}{2}=-\frac{1}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{18}{2}\right)x=-\frac{1}{2}$$

-18 ni 2 ga bo'lish.

$$x^{2}-9x=-\frac{1}{2}$$

-9 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{2} olish uchun. Keyin, -\frac{9}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-9x+\left(-\frac{9}{2}\right)^{2}=-\frac{1}{2}+\left(-\frac{9}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{2} kvadratini chiqarish.

$$x^{2}-9x+\frac{81}{4}=-\frac{1}{2}+\frac{81}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{2} ni \frac{81}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-9x+\frac{81}{4}=\frac{79}{4}$$

x^{2}-9x+\frac{81}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{9}{2}\right)^{2}=\frac{79}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{9}{2}\right)^{2}}=\sqrt{\frac{79}{4}}$$

Qisqartirish.

$$x-\frac{9}{2}=\frac{\sqrt{79}}{2} x-\frac{9}{2}=-\frac{\sqrt{79}}{2}$$

\frac{9}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{79}+9}{2} x=\frac{9-\sqrt{79}}{2}$$