289=4x^2 eching

$$289 = 4 x ^ { 2 }$$

x uchun yechish

$$x = \frac{17}{2} = 8\frac{1}{2} = 8,5$$

$$x = -\frac{17}{2} = -8\frac{1}{2} = -8,5$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 4 ga bo‘ling.

$$\frac{289}{4}=x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}=\frac{289}{4}$$

Ikkala tarafdan \frac{289}{4} ni ayirish.

$$x^{2}-\frac{289}{4}=0$$

Ikkala tarafini 4 ga ko‘paytiring.

$$4x^{2}-289=0$$

Hisoblang: 4x^{2}-289. 4x^{2}-289 ni \left(2x\right)^{2}-17^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-17\right)\left(2x+17\right)=0$$

Tenglamani yechish uchun 2x-17=0 va 2x+17=0 ni yeching.

$$x=\frac{17}{2} x=-\frac{17}{2}$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 4 ga bo‘ling.

$$\frac{289}{4}=x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}=\frac{289}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{17}{2} x=-\frac{17}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 4 ga bo‘ling.

$$\frac{289}{4}=x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}=\frac{289}{4}$$

Ikkala tarafdan \frac{289}{4} ni ayirish.

$$x^{2}-\frac{289}{4}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -\frac{289}{4} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{289}{4}\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{289}{4}\right)}}{2}$$

-4 ni -\frac{289}{4} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{289}}{2}$$

289 ning kvadrat ildizini chiqarish.

$$x=\frac{0±17}{2}$$

x=\frac{0±17}{2} tenglamasini yeching, bunda ± musbat. 17 ni 2 ga bo'lish.

$$x=\frac{17}{2}$$

x=\frac{0±17}{2} tenglamasini yeching, bunda ± manfiy. -17 ni 2 ga bo'lish.

$$x=-\frac{17}{2}$$

Tenglama yechildi.

$$x=\frac{17}{2} x=-\frac{17}{2}$$