5x*10-9xdiv2x=99 eching

$$5x \times 10-9x \div 2x=99$$

x uchun yechish

$$x = \frac{\sqrt{718} + 50}{9} \approx 8,532835779$$

$$x = \frac{50 - \sqrt{718}}{9} \approx 2,578275332$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$10x\times 10-9xx=198$$

100 hosil qilish uchun 10 va 10 ni ko'paytirish.

$$100x-9xx=198$$

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

$$100x-9x^{2}=198$$

Ikkala tarafdan 198 ni ayirish.

$$100x-9x^{2}-198=0$$

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.

$$-9x^{2}+100x-198=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -9 ni a, 100 ni b va -198 ni c bilan almashtiring.

$$x=\frac{-100±\sqrt{100^{2}-4\left(-9\right)\left(-198\right)}}{2\left(-9\right)}$$

100 kvadratini chiqarish.

$$x=\frac{-100±\sqrt{10000-4\left(-9\right)\left(-198\right)}}{2\left(-9\right)}$$

-4 ni -9 marotabaga ko'paytirish.

$$x=\frac{-100±\sqrt{10000+36\left(-198\right)}}{2\left(-9\right)}$$

36 ni -198 marotabaga ko'paytirish.

$$x=\frac{-100±\sqrt{10000-7128}}{2\left(-9\right)}$$

10000 ni -7128 ga qo'shish.

$$x=\frac{-100±\sqrt{2872}}{2\left(-9\right)}$$

2872 ning kvadrat ildizini chiqarish.

$$x=\frac{-100±2\sqrt{718}}{2\left(-9\right)}$$

2 ni -9 marotabaga ko'paytirish.

$$x=\frac{-100±2\sqrt{718}}{-18}$$

x=\frac{-100±2\sqrt{718}}{-18} tenglamasini yeching, bunda ± musbat. -100 ni 2\sqrt{718} ga qo'shish.

$$x=\frac{2\sqrt{718}-100}{-18}$$

-100+2\sqrt{718} ni -18 ga bo'lish.

$$x=\frac{50-\sqrt{718}}{9}$$

x=\frac{-100±2\sqrt{718}}{-18} tenglamasini yeching, bunda ± manfiy. -100 dan 2\sqrt{718} ni ayirish.

$$x=\frac{-2\sqrt{718}-100}{-18}$$

-100-2\sqrt{718} ni -18 ga bo'lish.

$$x=\frac{\sqrt{718}+50}{9}$$

Tenglama yechildi.

$$x=\frac{50-\sqrt{718}}{9} x=\frac{\sqrt{718}+50}{9}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$10x\times 10-9xx=198$$

100 hosil qilish uchun 10 va 10 ni ko'paytirish.

$$100x-9xx=198$$

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

$$100x-9x^{2}=198$$

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

$$-9x^{2}+100x=198$$

Ikki tarafini -9 ga bo‘ling.

$$\frac{-9x^{2}+100x}{-9}=\frac{198}{-9}$$

-9 ga bo'lish -9 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{100}{-9}x=\frac{198}{-9}$$

100 ni -9 ga bo'lish.

$$x^{2}-\frac{100}{9}x=\frac{198}{-9}$$

198 ni -9 ga bo'lish.

$$x^{2}-\frac{100}{9}x=-22$$

-\frac{100}{9} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{50}{9} olish uchun. Keyin, -\frac{50}{9} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{100}{9}x+\left(-\frac{50}{9}\right)^{2}=-22+\left(-\frac{50}{9}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{50}{9} kvadratini chiqarish.

$$x^{2}-\frac{100}{9}x+\frac{2500}{81}=-22+\frac{2500}{81}$$

-22 ni \frac{2500}{81} ga qo'shish.

$$x^{2}-\frac{100}{9}x+\frac{2500}{81}=\frac{718}{81}$$

x^{2}-\frac{100}{9}x+\frac{2500}{81} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{50}{9}\right)^{2}=\frac{718}{81}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{50}{9}\right)^{2}}=\sqrt{\frac{718}{81}}$$

Qisqartirish.

$$x-\frac{50}{9}=\frac{\sqrt{718}}{9} x-\frac{50}{9}=-\frac{\sqrt{718}}{9}$$

\frac{50}{9} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{718}+50}{9} x=\frac{50-\sqrt{718}}{9}$$