x=1/4x= eching

$$x= \frac{ 1 }{ 4x } =$$

x uchun yechish

$$x=\frac{1}{2}=0,5$$

$$x=-\frac{1}{2}=-0,5$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan \frac{1}{4x} ni ayirish.

$$x-\frac{1}{4x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{4x}{4x} marotabaga ko'paytirish.

$$\frac{x\times 4x}{4x}-\frac{1}{4x}=0$$

\frac{x\times 4x}{4x} va \frac{1}{4x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x\times 4x-1}{4x}=0$$

x\times 4x-1 ichidagi ko‘paytirishlarni bajaring.

$$\frac{4x^{2}-1}{4x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4x ga ko'paytirish.

$$4x^{2}-1=0$$

Hisoblang: 4x^{2}-1. 4x^{2}-1 ni \left(2x\right)^{2}-1^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-1\right)\left(2x+1\right)=0$$

Tenglamani yechish uchun 2x-1=0 va 2x+1=0 ni yeching.

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

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan \frac{1}{4x} ni ayirish.

$$x-\frac{1}{4x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{4x}{4x} marotabaga ko'paytirish.

$$\frac{x\times 4x}{4x}-\frac{1}{4x}=0$$

\frac{x\times 4x}{4x} va \frac{1}{4x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x\times 4x-1}{4x}=0$$

x\times 4x-1 ichidagi ko‘paytirishlarni bajaring.

$$\frac{4x^{2}-1}{4x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4x ga ko'paytirish.

$$4x^{2}-1=0$$

1 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$4x^{2}=1$$

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan \frac{1}{4x} ni ayirish.

$$x-\frac{1}{4x}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{4x}{4x} marotabaga ko'paytirish.

$$\frac{x\times 4x}{4x}-\frac{1}{4x}=0$$

\frac{x\times 4x}{4x} va \frac{1}{4x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x\times 4x-1}{4x}=0$$

x\times 4x-1 ichidagi ko‘paytirishlarni bajaring.

$$\frac{4x^{2}-1}{4x}=0$$

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4x ga ko'paytirish.

$$4x^{2}-1=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-1\right)}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4\left(-1\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\left(-1\right)}}{2\times 4}$$

-16 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{16}}{2\times 4}$$

16 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±4}{8}$$

x=\frac{0±4}{8} tenglamasini yeching, bunda ± musbat. \frac{4}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{2}$$

x=\frac{0±4}{8} tenglamasini yeching, bunda ± manfiy. \frac{-4}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

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