36x^2+80x-80=0 eching

$$36 { x }^{ 2 } +80x-80=0$$

x uchun yechish

$$x=\frac{2\sqrt{70}-10}{9}\approx 0,748133392$$

$$x=\frac{-2\sqrt{70}-10}{9}\approx -2,970355615$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$36x^{2}+80x-80=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 36 ni a, 80 ni b va -80 ni c bilan almashtiring.

$$x=\frac{-80±\sqrt{80^{2}-4\times 36\left(-80\right)}}{2\times 36}$$

80 kvadratini chiqarish.

$$x=\frac{-80±\sqrt{6400-4\times 36\left(-80\right)}}{2\times 36}$$

-4 ni 36 marotabaga ko'paytirish.

$$x=\frac{-80±\sqrt{6400-144\left(-80\right)}}{2\times 36}$$

-144 ni -80 marotabaga ko'paytirish.

$$x=\frac{-80±\sqrt{6400+11520}}{2\times 36}$$

6400 ni 11520 ga qo'shish.

$$x=\frac{-80±\sqrt{17920}}{2\times 36}$$

17920 ning kvadrat ildizini chiqarish.

$$x=\frac{-80±16\sqrt{70}}{2\times 36}$$

2 ni 36 marotabaga ko'paytirish.

$$x=\frac{-80±16\sqrt{70}}{72}$$

x=\frac{-80±16\sqrt{70}}{72} tenglamasini yeching, bunda ± musbat. -80 ni 16\sqrt{70} ga qo'shish.

$$x=\frac{16\sqrt{70}-80}{72}$$

-80+16\sqrt{70} ni 72 ga bo'lish.

$$x=\frac{2\sqrt{70}-10}{9}$$

x=\frac{-80±16\sqrt{70}}{72} tenglamasini yeching, bunda ± manfiy. -80 dan 16\sqrt{70} ni ayirish.

$$x=\frac{-16\sqrt{70}-80}{72}$$

-80-16\sqrt{70} ni 72 ga bo'lish.

$$x=\frac{-2\sqrt{70}-10}{9}$$

Tenglama yechildi.

$$x=\frac{2\sqrt{70}-10}{9} x=\frac{-2\sqrt{70}-10}{9}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$36x^{2}+80x-80=0$$

80 ni tenglamaning ikkala tarafiga qo'shish.

$$36x^{2}+80x-80-\left(-80\right)=-\left(-80\right)$$

O‘zidan -80 ayirilsa 0 qoladi.

$$36x^{2}+80x=-\left(-80\right)$$

0 dan -80 ni ayirish.

$$36x^{2}+80x=80$$

Ikki tarafini 36 ga bo‘ling.

$$\frac{36x^{2}+80x}{36}=\frac{80}{36}$$

36 ga bo'lish 36 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{80}{36}x=\frac{80}{36}$$

\frac{80}{36} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{20}{9}x=\frac{80}{36}$$

\frac{80}{36} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{20}{9}x=\frac{20}{9}$$

\frac{20}{9} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{10}{9} olish uchun. Keyin, \frac{10}{9} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{20}{9}x+\left(\frac{10}{9}\right)^{2}=\frac{20}{9}+\left(\frac{10}{9}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{10}{9} kvadratini chiqarish.

$$x^{2}+\frac{20}{9}x+\frac{100}{81}=\frac{20}{9}+\frac{100}{81}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{20}{9} ni \frac{100}{81} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{20}{9}x+\frac{100}{81}=\frac{280}{81}$$

x^{2}+\frac{20}{9}x+\frac{100}{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.

$$\left(x+\frac{10}{9}\right)^{2}=\frac{280}{81}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{10}{9}\right)^{2}}=\sqrt{\frac{280}{81}}$$

Qisqartirish.

$$x+\frac{10}{9}=\frac{2\sqrt{70}}{9} x+\frac{10}{9}=-\frac{2\sqrt{70}}{9}$$

Tenglamaning ikkala tarafidan \frac{10}{9} ni ayirish.

$$x=\frac{2\sqrt{70}-10}{9} x=\frac{-2\sqrt{70}-10}{9}$$