left(16-2xright)left(9-xright)=112 eching

$$\left( 16-2x \right) \left( 9-x \right) = 112$$

x uchun yechish

$$x=1$$

$$x=16$$

Kvadrat tenglamalaridan foydalanish qoidalari

16-2x ga 9-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$144-34x+2x^{2}=112$$

Ikkala tarafdan 112 ni ayirish.

$$144-34x+2x^{2}-112=0$$

32 olish uchun 144 dan 112 ni ayirish.

$$32-34x+2x^{2}=0$$

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.

$$2x^{2}-34x+32=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -34 ni b va 32 ni c bilan almashtiring.

$$x=\frac{-\left(-34\right)±\sqrt{\left(-34\right)^{2}-4\times 2\times 32}}{2\times 2}$$

-34 kvadratini chiqarish.

$$x=\frac{-\left(-34\right)±\sqrt{1156-4\times 2\times 32}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-34\right)±\sqrt{1156-8\times 32}}{2\times 2}$$

-8 ni 32 marotabaga ko'paytirish.

$$x=\frac{-\left(-34\right)±\sqrt{1156-256}}{2\times 2}$$

1156 ni -256 ga qo'shish.

$$x=\frac{-\left(-34\right)±\sqrt{900}}{2\times 2}$$

900 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-34\right)±30}{2\times 2}$$

-34 ning teskarisi 34 ga teng.

$$x=\frac{34±30}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{34±30}{4}$$

x=\frac{34±30}{4} tenglamasini yeching, bunda ± musbat. 34 ni 30 ga qo'shish.

$$x=\frac{64}{4}$$

64 ni 4 ga bo'lish.

$$x=16$$

x=\frac{34±30}{4} tenglamasini yeching, bunda ± manfiy. 34 dan 30 ni ayirish.

$$x=\frac{4}{4}$$

4 ni 4 ga bo'lish.

$$x=1$$

Tenglama yechildi.

$$x=16 x=1$$

Kvadratni yakunlash bo'yicha qadamlar

16-2x ga 9-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$144-34x+2x^{2}=112$$

Ikkala tarafdan 144 ni ayirish.

$$-34x+2x^{2}=112-144$$

-32 olish uchun 112 dan 144 ni ayirish.

$$-34x+2x^{2}=-32$$

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

$$2x^{2}-34x=-32$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-34x}{2}=-\frac{32}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{34}{2}\right)x=-\frac{32}{2}$$

-34 ni 2 ga bo'lish.

$$x^{2}-17x=-\frac{32}{2}$$

-32 ni 2 ga bo'lish.

$$x^{2}-17x=-16$$

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

$$x^{2}-17x+\left(-\frac{17}{2}\right)^{2}=-16+\left(-\frac{17}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{17}{2} kvadratini chiqarish.

$$x^{2}-17x+\frac{289}{4}=-16+\frac{289}{4}$$

-16 ni \frac{289}{4} ga qo'shish.

$$x^{2}-17x+\frac{289}{4}=\frac{225}{4}$$

x^{2}-17x+\frac{289}{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.

$$\left(x-\frac{17}{2}\right)^{2}=\frac{225}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{17}{2}\right)^{2}}=\sqrt{\frac{225}{4}}$$

Qisqartirish.

$$x-\frac{17}{2}=\frac{15}{2} x-\frac{17}{2}=-\frac{15}{2}$$

\frac{17}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=16 x=1$$