(20-x)x=75 eching

$$(20-x)x=75$$

x uchun yechish

$$x=5$$

$$x=15$$

Kvadrat tenglamalaridan foydalanish qoidalari

20-x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$20x-x^{2}=75$$

Ikkala tarafdan 75 ni ayirish.

$$20x-x^{2}-75=0$$

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.

$$-x^{2}+20x-75=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 20 ni b va -75 ni c bilan almashtiring.

$$x=\frac{-20±\sqrt{20^{2}-4\left(-1\right)\left(-75\right)}}{2\left(-1\right)}$$

20 kvadratini chiqarish.

$$x=\frac{-20±\sqrt{400-4\left(-1\right)\left(-75\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400+4\left(-75\right)}}{2\left(-1\right)}$$

4 ni -75 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400-300}}{2\left(-1\right)}$$

400 ni -300 ga qo'shish.

$$x=\frac{-20±\sqrt{100}}{2\left(-1\right)}$$

100 ning kvadrat ildizini chiqarish.

$$x=\frac{-20±10}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-20±10}{-2}$$

x=\frac{-20±10}{-2} tenglamasini yeching, bunda ± musbat. -20 ni 10 ga qo'shish.

$$x=-\frac{10}{-2}$$

-10 ni -2 ga bo'lish.

$$x=5$$

x=\frac{-20±10}{-2} tenglamasini yeching, bunda ± manfiy. -20 dan 10 ni ayirish.

$$x=-\frac{30}{-2}$$

-30 ni -2 ga bo'lish.

$$x=15$$

Tenglama yechildi.

$$x=5 x=15$$

Kvadratni yakunlash bo'yicha qadamlar

20-x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$20x-x^{2}=75$$

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

$$-x^{2}+20x=75$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+20x}{-1}=\frac{75}{-1}$$

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

$$x^{2}+\frac{20}{-1}x=\frac{75}{-1}$$

20 ni -1 ga bo'lish.

$$x^{2}-20x=\frac{75}{-1}$$

75 ni -1 ga bo'lish.

$$x^{2}-20x=-75$$

-20 ni bo‘lish, x shartining koeffitsienti, 2 ga -10 olish uchun. Keyin, -10 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-20x+\left(-10\right)^{2}=-75+\left(-10\right)^{2}$$

-10 kvadratini chiqarish.

$$x^{2}-20x+100=-75+100$$

-75 ni 100 ga qo'shish.

$$x^{2}-20x+100=25$$

x^{2}-20x+100 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-10\right)^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-10\right)^{2}}=\sqrt{25}$$

Qisqartirish.

$$x-10=5 x-10=-5$$

10 ni tenglamaning ikkala tarafiga qo'shish.

$$x=15 x=5$$