150x-x^2=(1-08832)100*50 eching

$$150x- { x }^{ 2 } =(1-08832)100 \times 50$$

x uchun yechish

$$x=50$$

$$x=100$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 8832 ni ko'paytirish.

$$150x-x^{2}=\left(1-0\right)\times 100\times 50$$

1 olish uchun 1 dan 0 ni ayirish.

$$150x-x^{2}=1\times 100\times 50$$

100 hosil qilish uchun 1 va 100 ni ko'paytirish.

$$150x-x^{2}=100\times 50$$

5000 hosil qilish uchun 100 va 50 ni ko'paytirish.

$$150x-x^{2}=5000$$

Ikkala tarafdan 5000 ni ayirish.

$$150x-x^{2}-5000=0$$

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.

$$-x^{2}+150x-5000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 150 ni b va -5000 ni c bilan almashtiring.

$$x=\frac{-150±\sqrt{150^{2}-4\left(-1\right)\left(-5000\right)}}{2\left(-1\right)}$$

150 kvadratini chiqarish.

$$x=\frac{-150±\sqrt{22500-4\left(-1\right)\left(-5000\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-150±\sqrt{22500+4\left(-5000\right)}}{2\left(-1\right)}$$

4 ni -5000 marotabaga ko'paytirish.

$$x=\frac{-150±\sqrt{22500-20000}}{2\left(-1\right)}$$

22500 ni -20000 ga qo'shish.

$$x=\frac{-150±\sqrt{2500}}{2\left(-1\right)}$$

2500 ning kvadrat ildizini chiqarish.

$$x=\frac{-150±50}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-150±50}{-2}$$

x=\frac{-150±50}{-2} tenglamasini yeching, bunda ± musbat. -150 ni 50 ga qo'shish.

$$x=-\frac{100}{-2}$$

-100 ni -2 ga bo'lish.

$$x=50$$

x=\frac{-150±50}{-2} tenglamasini yeching, bunda ± manfiy. -150 dan 50 ni ayirish.

$$x=-\frac{200}{-2}$$

-200 ni -2 ga bo'lish.

$$x=100$$

Tenglama yechildi.

$$x=50 x=100$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 8832 ni ko'paytirish.

$$150x-x^{2}=\left(1-0\right)\times 100\times 50$$

1 olish uchun 1 dan 0 ni ayirish.

$$150x-x^{2}=1\times 100\times 50$$

100 hosil qilish uchun 1 va 100 ni ko'paytirish.

$$150x-x^{2}=100\times 50$$

5000 hosil qilish uchun 100 va 50 ni ko'paytirish.

$$150x-x^{2}=5000$$

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

$$-x^{2}+150x=5000$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+150x}{-1}=\frac{5000}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{150}{-1}x=\frac{5000}{-1}$$

150 ni -1 ga bo'lish.

$$x^{2}-150x=\frac{5000}{-1}$$

5000 ni -1 ga bo'lish.

$$x^{2}-150x=-5000$$

-150 ni bo‘lish, x shartining koeffitsienti, 2 ga -75 olish uchun. Keyin, -75 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-150x+\left(-75\right)^{2}=-5000+\left(-75\right)^{2}$$

-75 kvadratini chiqarish.

$$x^{2}-150x+5625=-5000+5625$$

-5000 ni 5625 ga qo'shish.

$$x^{2}-150x+5625=625$$

x^{2}-150x+5625 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-75\right)^{2}=625$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-75\right)^{2}}=\sqrt{625}$$

Qisqartirish.

$$x-75=25 x-75=-25$$

75 ni tenglamaning ikkala tarafiga qo'shish.

$$x=100 x=50$$