34-x=288/x eching

$$34 - x = \frac { 288 } { x }$$

x uchun yechish

$$x=16$$

$$x=18$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x\times 34-xx=288$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x\times 34-x^{2}=288$$

Ikkala tarafdan 288 ni ayirish.

$$x\times 34-x^{2}-288=0$$

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.

$$-x^{2}+34x-288=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 34 ni b va -288 ni c bilan almashtiring.

$$x=\frac{-34±\sqrt{34^{2}-4\left(-1\right)\left(-288\right)}}{2\left(-1\right)}$$

34 kvadratini chiqarish.

$$x=\frac{-34±\sqrt{1156-4\left(-1\right)\left(-288\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-34±\sqrt{1156+4\left(-288\right)}}{2\left(-1\right)}$$

4 ni -288 marotabaga ko'paytirish.

$$x=\frac{-34±\sqrt{1156-1152}}{2\left(-1\right)}$$

1156 ni -1152 ga qo'shish.

$$x=\frac{-34±\sqrt{4}}{2\left(-1\right)}$$

4 ning kvadrat ildizini chiqarish.

$$x=\frac{-34±2}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-34±2}{-2}$$

x=\frac{-34±2}{-2} tenglamasini yeching, bunda ± musbat. -34 ni 2 ga qo'shish.

$$x=-\frac{32}{-2}$$

-32 ni -2 ga bo'lish.

$$x=16$$

x=\frac{-34±2}{-2} tenglamasini yeching, bunda ± manfiy. -34 dan 2 ni ayirish.

$$x=-\frac{36}{-2}$$

-36 ni -2 ga bo'lish.

$$x=18$$

Tenglama yechildi.

$$x=16 x=18$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$x\times 34-xx=288$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x\times 34-x^{2}=288$$

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

$$-x^{2}+34x=288$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+34x}{-1}=\frac{288}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{34}{-1}x=\frac{288}{-1}$$

34 ni -1 ga bo'lish.

$$x^{2}-34x=\frac{288}{-1}$$

288 ni -1 ga bo'lish.

$$x^{2}-34x=-288$$

-34 ni bo‘lish, x shartining koeffitsienti, 2 ga -17 olish uchun. Keyin, -17 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-34x+\left(-17\right)^{2}=-288+\left(-17\right)^{2}$$

-17 kvadratini chiqarish.

$$x^{2}-34x+289=-288+289$$

-288 ni 289 ga qo'shish.

$$x^{2}-34x+289=1$$

x^{2}-34x+289 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-17\right)^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-17\right)^{2}}=\sqrt{1}$$

Qisqartirish.

$$x-17=1 x-17=-1$$

17 ni tenglamaning ikkala tarafiga qo'shish.

$$x=18 x=16$$