(t-6)(t-8)=24 eching

$$( t - 6 ) ( t - 8 ) = 24$$

t uchun yechish

$$t=2$$

$$t=12$$

Kvadrat tenglamalaridan foydalanish qoidalari

t-6 ga t-8 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$t^{2}-14t+48=24$$

Ikkala tarafdan 24 ni ayirish.

$$t^{2}-14t+48-24=0$$

24 olish uchun 48 dan 24 ni ayirish.

$$t^{2}-14t+24=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -14 ni b va 24 ni c bilan almashtiring.

$$t=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 24}}{2}$$

-14 kvadratini chiqarish.

$$t=\frac{-\left(-14\right)±\sqrt{196-4\times 24}}{2}$$

-4 ni 24 marotabaga ko'paytirish.

$$t=\frac{-\left(-14\right)±\sqrt{196-96}}{2}$$

196 ni -96 ga qo'shish.

$$t=\frac{-\left(-14\right)±\sqrt{100}}{2}$$

100 ning kvadrat ildizini chiqarish.

$$t=\frac{-\left(-14\right)±10}{2}$$

-14 ning teskarisi 14 ga teng.

$$t=\frac{14±10}{2}$$

t=\frac{14±10}{2} tenglamasini yeching, bunda ± musbat. 14 ni 10 ga qo'shish.

$$t=\frac{24}{2}$$

24 ni 2 ga bo'lish.

$$t=12$$

t=\frac{14±10}{2} tenglamasini yeching, bunda ± manfiy. 14 dan 10 ni ayirish.

$$t=\frac{4}{2}$$

4 ni 2 ga bo'lish.

$$t=2$$

Tenglama yechildi.

$$t=12 t=2$$

Kvadratni yakunlash bo'yicha qadamlar

t-6 ga t-8 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$t^{2}-14t+48=24$$

Ikkala tarafdan 48 ni ayirish.

$$t^{2}-14t=24-48$$

-24 olish uchun 24 dan 48 ni ayirish.

$$t^{2}-14t=-24$$

-14 ni bo‘lish, x shartining koeffitsienti, 2 ga -7 olish uchun. Keyin, -7 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-14t+\left(-7\right)^{2}=-24+\left(-7\right)^{2}$$

-7 kvadratini chiqarish.

$$t^{2}-14t+49=-24+49$$

-24 ni 49 ga qo'shish.

$$t^{2}-14t+49=25$$

t^{2}-14t+49 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t-7\right)^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-7\right)^{2}}=\sqrt{25}$$

Qisqartirish.

$$t-7=5 t-7=-5$$

7 ni tenglamaning ikkala tarafiga qo'shish.

$$t=12 t=2$$