4z^2+160z=600 eching

$$4 { z }^{ 2 } +160z = 600$$

z uchun yechish

$$z=5\sqrt{22}-20\approx 3,452078799$$

$$z=-5\sqrt{22}-20\approx -43,452078799$$

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.

$$4z^{2}+160z=600$$

Tenglamaning ikkala tarafidan 600 ni ayirish.

$$4z^{2}+160z-600=600-600$$

O‘zidan 600 ayirilsa 0 qoladi.

$$4z^{2}+160z-600=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 160 ni b va -600 ni c bilan almashtiring.

$$z=\frac{-160±\sqrt{160^{2}-4\times 4\left(-600\right)}}{2\times 4}$$

160 kvadratini chiqarish.

$$z=\frac{-160±\sqrt{25600-4\times 4\left(-600\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$z=\frac{-160±\sqrt{25600-16\left(-600\right)}}{2\times 4}$$

-16 ni -600 marotabaga ko'paytirish.

$$z=\frac{-160±\sqrt{25600+9600}}{2\times 4}$$

25600 ni 9600 ga qo'shish.

$$z=\frac{-160±\sqrt{35200}}{2\times 4}$$

35200 ning kvadrat ildizini chiqarish.

$$z=\frac{-160±40\sqrt{22}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$z=\frac{-160±40\sqrt{22}}{8}$$

z=\frac{-160±40\sqrt{22}}{8} tenglamasini yeching, bunda ± musbat. -160 ni 40\sqrt{22} ga qo'shish.

$$z=\frac{40\sqrt{22}-160}{8}$$

-160+40\sqrt{22} ni 8 ga bo'lish.

$$z=5\sqrt{22}-20$$

z=\frac{-160±40\sqrt{22}}{8} tenglamasini yeching, bunda ± manfiy. -160 dan 40\sqrt{22} ni ayirish.

$$z=\frac{-40\sqrt{22}-160}{8}$$

-160-40\sqrt{22} ni 8 ga bo'lish.

$$z=-5\sqrt{22}-20$$

Tenglama yechildi.

$$z=5\sqrt{22}-20 z=-5\sqrt{22}-20$$

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.

$$4z^{2}+160z=600$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4z^{2}+160z}{4}=\frac{600}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$z^{2}+\frac{160}{4}z=\frac{600}{4}$$

160 ni 4 ga bo'lish.

$$z^{2}+40z=\frac{600}{4}$$

600 ni 4 ga bo'lish.

$$z^{2}+40z=150$$

40 ni bo‘lish, x shartining koeffitsienti, 2 ga 20 olish uchun. Keyin, 20 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$z^{2}+40z+20^{2}=150+20^{2}$$

20 kvadratini chiqarish.

$$z^{2}+40z+400=150+400$$

150 ni 400 ga qo'shish.

$$z^{2}+40z+400=550$$

z^{2}+40z+400 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(z+20\right)^{2}=550$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(z+20\right)^{2}}=\sqrt{550}$$

Qisqartirish.

$$z+20=5\sqrt{22} z+20=-5\sqrt{22}$$

Tenglamaning ikkala tarafidan 20 ni ayirish.

$$z=5\sqrt{22}-20 z=-5\sqrt{22}-20$$