x*(-20x+920)=3100 eching

$$x \cdot ( - 20 x + 920 ) = 3100$$

x uchun yechish

$$x=\sqrt{374}+23\approx 42,339079606$$

$$x=23-\sqrt{374}\approx 3,660920394$$

Kvadrat tenglamalaridan foydalanish qoidalari

x ga -20x+920 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-20x^{2}+920x=3100$$

Ikkala tarafdan 3100 ni ayirish.

$$-20x^{2}+920x-3100=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -20 ni a, 920 ni b va -3100 ni c bilan almashtiring.

$$x=\frac{-920±\sqrt{920^{2}-4\left(-20\right)\left(-3100\right)}}{2\left(-20\right)}$$

920 kvadratini chiqarish.

$$x=\frac{-920±\sqrt{846400-4\left(-20\right)\left(-3100\right)}}{2\left(-20\right)}$$

-4 ni -20 marotabaga ko'paytirish.

$$x=\frac{-920±\sqrt{846400+80\left(-3100\right)}}{2\left(-20\right)}$$

80 ni -3100 marotabaga ko'paytirish.

$$x=\frac{-920±\sqrt{846400-248000}}{2\left(-20\right)}$$

846400 ni -248000 ga qo'shish.

$$x=\frac{-920±\sqrt{598400}}{2\left(-20\right)}$$

598400 ning kvadrat ildizini chiqarish.

$$x=\frac{-920±40\sqrt{374}}{2\left(-20\right)}$$

2 ni -20 marotabaga ko'paytirish.

$$x=\frac{-920±40\sqrt{374}}{-40}$$

x=\frac{-920±40\sqrt{374}}{-40} tenglamasini yeching, bunda ± musbat. -920 ni 40\sqrt{374} ga qo'shish.

$$x=\frac{40\sqrt{374}-920}{-40}$$

-920+40\sqrt{374} ni -40 ga bo'lish.

$$x=23-\sqrt{374}$$

x=\frac{-920±40\sqrt{374}}{-40} tenglamasini yeching, bunda ± manfiy. -920 dan 40\sqrt{374} ni ayirish.

$$x=\frac{-40\sqrt{374}-920}{-40}$$

-920-40\sqrt{374} ni -40 ga bo'lish.

$$x=\sqrt{374}+23$$

Tenglama yechildi.

$$x=23-\sqrt{374} x=\sqrt{374}+23$$

Kvadratni yakunlash bo'yicha qadamlar

x ga -20x+920 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-20x^{2}+920x=3100$$

Ikki tarafini -20 ga bo‘ling.

$$\frac{-20x^{2}+920x}{-20}=\frac{3100}{-20}$$

-20 ga bo'lish -20 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{920}{-20}x=\frac{3100}{-20}$$

920 ni -20 ga bo'lish.

$$x^{2}-46x=\frac{3100}{-20}$$

3100 ni -20 ga bo'lish.

$$x^{2}-46x=-155$$

-46 ni bo‘lish, x shartining koeffitsienti, 2 ga -23 olish uchun. Keyin, -23 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-46x+\left(-23\right)^{2}=-155+\left(-23\right)^{2}$$

-23 kvadratini chiqarish.

$$x^{2}-46x+529=-155+529$$

-155 ni 529 ga qo'shish.

$$x^{2}-46x+529=374$$

x^{2}-46x+529 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-23\right)^{2}=374$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-23\right)^{2}}=\sqrt{374}$$

Qisqartirish.

$$x-23=\sqrt{374} x-23=-\sqrt{374}$$

23 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{374}+23 x=23-\sqrt{374}$$