-270x=30x^2 eching

$$- 270 x = 30 x ^ { 2 }$$

x uchun yechish

$$x=-9$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 30x^{2} ni ayirish.

$$-270x-30x^{2}=0$$

x omili.

$$x\left(-270-30x\right)=0$$

Tenglamani yechish uchun x=0 va -270-30x=0 ni yeching.

$$x=0 x=-9$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 30x^{2} ni ayirish.

$$-270x-30x^{2}=0$$

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.

$$-30x^{2}-270x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -30 ni a, -270 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-270\right)±\sqrt{\left(-270\right)^{2}}}{2\left(-30\right)}$$

\left(-270\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-270\right)±270}{2\left(-30\right)}$$

-270 ning teskarisi 270 ga teng.

$$x=\frac{270±270}{2\left(-30\right)}$$

2 ni -30 marotabaga ko'paytirish.

$$x=\frac{270±270}{-60}$$

x=\frac{270±270}{-60} tenglamasini yeching, bunda ± musbat. 270 ni 270 ga qo'shish.

$$x=\frac{540}{-60}$$

540 ni -60 ga bo'lish.

$$x=-9$$

x=\frac{270±270}{-60} tenglamasini yeching, bunda ± manfiy. 270 dan 270 ni ayirish.

$$x=\frac{0}{-60}$$

0 ni -60 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-9 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 30x^{2} ni ayirish.

$$-270x-30x^{2}=0$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-30x^{2}-270x=0$$

Ikki tarafini -30 ga bo‘ling.

$$\frac{-30x^{2}-270x}{-30}=\frac{0}{-30}$$

-30 ga bo'lish -30 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{270}{-30}\right)x=\frac{0}{-30}$$

-270 ni -30 ga bo'lish.

$$x^{2}+9x=\frac{0}{-30}$$

0 ni -30 ga bo'lish.

$$x^{2}+9x=0$$

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.

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

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

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

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.

$$\left(x+\frac{9}{2}\right)^{2}=\frac{81}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{9}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Qisqartirish.

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

Tenglamaning ikkala tarafidan \frac{9}{2} ni ayirish.

$$x=0 x=-9$$