30x-16sqrt{x}+2=0 eching

$$30x-16 \sqrt{ x } +2=0$$

x uchun yechish

$$x=\frac{1}{9}\approx 0,111111111$$

$$x=\frac{1}{25}=0,04$$

Yechim qadamlari

Ikkala tarafdan 2 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$30x-16\sqrt{x}=-2$$

Tenglamaning ikkala tarafidan 30x ni ayirish.

$$-16\sqrt{x}=-2-30x$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(-16\sqrt{x}\right)^{2}=\left(-2-30x\right)^{2}$$

\left(-16\sqrt{x}\right)^{2} ni kengaytirish.

$$\left(-16\right)^{2}\left(\sqrt{x}\right)^{2}=\left(-2-30x\right)^{2}$$

2 daraja ko‘rsatkichini -16 ga hisoblang va 256 ni qiymatni oling.

$$256\left(\sqrt{x}\right)^{2}=\left(-2-30x\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{x} ga hisoblang va x ni qiymatni oling.

$$256x=\left(-2-30x\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(-2-30x\right)^{2} kengaytirilishi uchun ishlating.

$$256x=4+120x+900x^{2}$$

Ikkala tarafdan 120x ni ayirish.

$$256x-120x=4+900x^{2}$$

136x ni olish uchun 256x va -120x ni birlashtirish.

$$136x=4+900x^{2}$$

Ikkala tarafdan 900x^{2} ni ayirish.

$$136x-900x^{2}=4$$

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.

$$-900x^{2}+136x=4$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$-900x^{2}+136x-4=4-4$$

O‘zidan 4 ayirilsa 0 qoladi.

$$-900x^{2}+136x-4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -900 ni a, 136 ni b va -4 ni c bilan almashtiring.

$$x=\frac{-136±\sqrt{136^{2}-4\left(-900\right)\left(-4\right)}}{2\left(-900\right)}$$

136 kvadratini chiqarish.

$$x=\frac{-136±\sqrt{18496-4\left(-900\right)\left(-4\right)}}{2\left(-900\right)}$$

-4 ni -900 marotabaga ko'paytirish.

$$x=\frac{-136±\sqrt{18496+3600\left(-4\right)}}{2\left(-900\right)}$$

3600 ni -4 marotabaga ko'paytirish.

$$x=\frac{-136±\sqrt{18496-14400}}{2\left(-900\right)}$$

18496 ni -14400 ga qo'shish.

$$x=\frac{-136±\sqrt{4096}}{2\left(-900\right)}$$

4096 ning kvadrat ildizini chiqarish.

$$x=\frac{-136±64}{2\left(-900\right)}$$

2 ni -900 marotabaga ko'paytirish.

$$x=\frac{-136±64}{-1800}$$

x=\frac{-136±64}{-1800} tenglamasini yeching, bunda ± musbat. -136 ni 64 ga qo'shish.

$$x=-\frac{72}{-1800}$$

\frac{-72}{-1800} ulushini 72 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{25}$$

x=\frac{-136±64}{-1800} tenglamasini yeching, bunda ± manfiy. -136 dan 64 ni ayirish.

$$x=-\frac{200}{-1800}$$

\frac{-200}{-1800} ulushini 200 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{9}$$

Tenglama yechildi.

$$x=\frac{1}{25} x=\frac{1}{9}$$

30x-16\sqrt{x}+2=0 tenglamasida x uchun \frac{1}{25} ni almashtiring.

$$30\times \frac{1}{25}-16\sqrt{\frac{1}{25}}+2=0$$

Qisqartirish. x=\frac{1}{25} tenglamani qoniqtiradi.

$$0=0$$

30x-16\sqrt{x}+2=0 tenglamasida x uchun \frac{1}{9} ni almashtiring.

$$30\times \frac{1}{9}-16\sqrt{\frac{1}{9}}+2=0$$

Qisqartirish. x=\frac{1}{9} tenglamani qoniqtiradi.

$$0=0$$

-16\sqrt{x}=-30x-2 boʻyicha barcha yechimlar roʻyxati.

$$x=\frac{1}{25} x=\frac{1}{9}$$