t^2-2t-3=-4+t-3 eching

$$t ^ { 2 } - 2 t - 3 = - 4 + t - 3$$

t uchun yechish

$$t=\frac{3+\sqrt{7}i}{2}\approx 1,5+1,322875656i$$

$$t=\frac{-\sqrt{7}i+3}{2}\approx 1,5-1,322875656i$$

Kvadrat tenglamalaridan foydalanish qoidalari

-7 olish uchun -4 dan 3 ni ayirish.

$$t^{2}-2t-3=-7+t$$

Ikkala tarafdan -7 ni ayirish.

$$t^{2}-2t-3-\left(-7\right)=t$$

-7 ning teskarisi 7 ga teng.

$$t^{2}-2t-3+7=t$$

Ikkala tarafdan t ni ayirish.

$$t^{2}-2t-3+7-t=0$$

4 olish uchun -3 va 7'ni qo'shing.

$$t^{2}-2t+4-t=0$$

-3t ni olish uchun -2t va -t ni birlashtirish.

$$t^{2}-3t+4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va 4 ni c bilan almashtiring.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 4}}{2}$$

-3 kvadratini chiqarish.

$$t=\frac{-\left(-3\right)±\sqrt{9-4\times 4}}{2}$$

-4 ni 4 marotabaga ko'paytirish.

$$t=\frac{-\left(-3\right)±\sqrt{9-16}}{2}$$

9 ni -16 ga qo'shish.

$$t=\frac{-\left(-3\right)±\sqrt{-7}}{2}$$

-7 ning kvadrat ildizini chiqarish.

$$t=\frac{-\left(-3\right)±\sqrt{7}i}{2}$$

-3 ning teskarisi 3 ga teng.

$$t=\frac{3±\sqrt{7}i}{2}$$

t=\frac{3±\sqrt{7}i}{2} tenglamasini yeching, bunda ± musbat. 3 ni i\sqrt{7} ga qo'shish.

$$t=\frac{3+\sqrt{7}i}{2}$$

t=\frac{3±\sqrt{7}i}{2} tenglamasini yeching, bunda ± manfiy. 3 dan i\sqrt{7} ni ayirish.

$$t=\frac{-\sqrt{7}i+3}{2}$$

Tenglama yechildi.

$$t=\frac{3+\sqrt{7}i}{2} t=\frac{-\sqrt{7}i+3}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

-7 olish uchun -4 dan 3 ni ayirish.

$$t^{2}-2t-3=-7+t$$

Ikkala tarafdan t ni ayirish.

$$t^{2}-2t-3-t=-7$$

-3t ni olish uchun -2t va -t ni birlashtirish.

$$t^{2}-3t-3=-7$$

3 ni ikki tarafga qo’shing.

$$t^{2}-3t=-7+3$$

-4 olish uchun -7 va 3'ni qo'shing.

$$t^{2}-3t=-4$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-3t+\left(-\frac{3}{2}\right)^{2}=-4+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$t^{2}-3t+\frac{9}{4}=-4+\frac{9}{4}$$

-4 ni \frac{9}{4} ga qo'shish.

$$t^{2}-3t+\frac{9}{4}=-\frac{7}{4}$$

t^{2}-3t+\frac{9}{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.

$$\left(t-\frac{3}{2}\right)^{2}=-\frac{7}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-\frac{3}{2}\right)^{2}}=\sqrt{-\frac{7}{4}}$$

Qisqartirish.

$$t-\frac{3}{2}=\frac{\sqrt{7}i}{2} t-\frac{3}{2}=-\frac{\sqrt{7}i}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$t=\frac{3+\sqrt{7}i}{2} t=\frac{-\sqrt{7}i+3}{2}$$