t^2-107t+900=0 eching

$$t ^ { 2 } - 107 t + 900 = 0$$

t uchun yechish

$$t = \frac{\sqrt{7849} + 107}{2} \approx 97,797291114$$

$$t = \frac{107 - \sqrt{7849}}{2} \approx 9,202708886$$

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.

$$t^{2}-107t+900=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -107 ni b va 900 ni c bilan almashtiring.

$$t=\frac{-\left(-107\right)±\sqrt{\left(-107\right)^{2}-4\times 900}}{2}$$

-107 kvadratini chiqarish.

$$t=\frac{-\left(-107\right)±\sqrt{11449-4\times 900}}{2}$$

-4 ni 900 marotabaga ko'paytirish.

$$t=\frac{-\left(-107\right)±\sqrt{11449-3600}}{2}$$

11449 ni -3600 ga qo'shish.

$$t=\frac{-\left(-107\right)±\sqrt{7849}}{2}$$

-107 ning teskarisi 107 ga teng.

$$t=\frac{107±\sqrt{7849}}{2}$$

t=\frac{107±\sqrt{7849}}{2} tenglamasini yeching, bunda ± musbat. 107 ni \sqrt{7849} ga qo'shish.

$$t=\frac{\sqrt{7849}+107}{2}$$

t=\frac{107±\sqrt{7849}}{2} tenglamasini yeching, bunda ± manfiy. 107 dan \sqrt{7849} ni ayirish.

$$t=\frac{107-\sqrt{7849}}{2}$$

Tenglama yechildi.

$$t=\frac{\sqrt{7849}+107}{2} t=\frac{107-\sqrt{7849}}{2}$$

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.

$$t^{2}-107t+900=0$$

Tenglamaning ikkala tarafidan 900 ni ayirish.

$$t^{2}-107t+900-900=-900$$

O‘zidan 900 ayirilsa 0 qoladi.

$$t^{2}-107t=-900$$

-107 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{107}{2} olish uchun. Keyin, -\frac{107}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-107t+\left(-\frac{107}{2}\right)^{2}=-900+\left(-\frac{107}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{107}{2} kvadratini chiqarish.

$$t^{2}-107t+\frac{11449}{4}=-900+\frac{11449}{4}$$

-900 ni \frac{11449}{4} ga qo'shish.

$$t^{2}-107t+\frac{11449}{4}=\frac{7849}{4}$$

t^{2}-107t+\frac{11449}{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.

$$\left(t-\frac{107}{2}\right)^{2}=\frac{7849}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-\frac{107}{2}\right)^{2}}=\sqrt{\frac{7849}{4}}$$

Qisqartirish.

$$t-\frac{107}{2}=\frac{\sqrt{7849}}{2} t-\frac{107}{2}=-\frac{\sqrt{7849}}{2}$$

\frac{107}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$t=\frac{\sqrt{7849}+107}{2} t=\frac{107-\sqrt{7849}}{2}$$