80b-b^2=1500 eching

$$80 b - b ^ { 2 } = 1500$$

b uchun yechish

$$b=30$$

$$b=50$$

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.

$$-b^{2}+80b=1500$$

Tenglamaning ikkala tarafidan 1500 ni ayirish.

$$-b^{2}+80b-1500=1500-1500$$

O‘zidan 1500 ayirilsa 0 qoladi.

$$-b^{2}+80b-1500=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 80 ni b va -1500 ni c bilan almashtiring.

$$b=\frac{-80±\sqrt{80^{2}-4\left(-1\right)\left(-1500\right)}}{2\left(-1\right)}$$

80 kvadratini chiqarish.

$$b=\frac{-80±\sqrt{6400-4\left(-1\right)\left(-1500\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$b=\frac{-80±\sqrt{6400+4\left(-1500\right)}}{2\left(-1\right)}$$

4 ni -1500 marotabaga ko'paytirish.

$$b=\frac{-80±\sqrt{6400-6000}}{2\left(-1\right)}$$

6400 ni -6000 ga qo'shish.

$$b=\frac{-80±\sqrt{400}}{2\left(-1\right)}$$

400 ning kvadrat ildizini chiqarish.

$$b=\frac{-80±20}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$b=\frac{-80±20}{-2}$$

b=\frac{-80±20}{-2} tenglamasini yeching, bunda ± musbat. -80 ni 20 ga qo'shish.

$$b=-\frac{60}{-2}$$

-60 ni -2 ga bo'lish.

$$b=30$$

b=\frac{-80±20}{-2} tenglamasini yeching, bunda ± manfiy. -80 dan 20 ni ayirish.

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

-100 ni -2 ga bo'lish.

$$b=50$$

Tenglama yechildi.

$$b=30 b=50$$

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.

$$-b^{2}+80b=1500$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-b^{2}+80b}{-1}=\frac{1500}{-1}$$

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

$$b^{2}+\frac{80}{-1}b=\frac{1500}{-1}$$

80 ni -1 ga bo'lish.

$$b^{2}-80b=\frac{1500}{-1}$$

1500 ni -1 ga bo'lish.

$$b^{2}-80b=-1500$$

-80 ni bo‘lish, x shartining koeffitsienti, 2 ga -40 olish uchun. Keyin, -40 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$b^{2}-80b+\left(-40\right)^{2}=-1500+\left(-40\right)^{2}$$

-40 kvadratini chiqarish.

$$b^{2}-80b+1600=-1500+1600$$

-1500 ni 1600 ga qo'shish.

$$b^{2}-80b+1600=100$$

b^{2}-80b+1600 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(b-40\right)^{2}=100$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(b-40\right)^{2}}=\sqrt{100}$$

Qisqartirish.

$$b-40=10 b-40=-10$$

40 ni tenglamaning ikkala tarafiga qo'shish.

$$b=50 b=30$$