160=-x^2+92x-1920 eching

$$160 = - { x }^{ 2 } +92x-1920$$

x uchun yechish

$$x=40$$

$$x=52$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-x^{2}+92x-1920=160$$

Ikkala tarafdan 160 ni ayirish.

$$-x^{2}+92x-1920-160=0$$

-2080 olish uchun -1920 dan 160 ni ayirish.

$$-x^{2}+92x-2080=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 92 ni b va -2080 ni c bilan almashtiring.

$$x=\frac{-92±\sqrt{92^{2}-4\left(-1\right)\left(-2080\right)}}{2\left(-1\right)}$$

92 kvadratini chiqarish.

$$x=\frac{-92±\sqrt{8464-4\left(-1\right)\left(-2080\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-92±\sqrt{8464+4\left(-2080\right)}}{2\left(-1\right)}$$

4 ni -2080 marotabaga ko'paytirish.

$$x=\frac{-92±\sqrt{8464-8320}}{2\left(-1\right)}$$

8464 ni -8320 ga qo'shish.

$$x=\frac{-92±\sqrt{144}}{2\left(-1\right)}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{-92±12}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-92±12}{-2}$$

x=\frac{-92±12}{-2} tenglamasini yeching, bunda ± musbat. -92 ni 12 ga qo'shish.

$$x=-\frac{80}{-2}$$

-80 ni -2 ga bo'lish.

$$x=40$$

x=\frac{-92±12}{-2} tenglamasini yeching, bunda ± manfiy. -92 dan 12 ni ayirish.

$$x=-\frac{104}{-2}$$

-104 ni -2 ga bo'lish.

$$x=52$$

Tenglama yechildi.

$$x=40 x=52$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-x^{2}+92x-1920=160$$

1920 ni ikki tarafga qo’shing.

$$-x^{2}+92x=160+1920$$

2080 olish uchun 160 va 1920'ni qo'shing.

$$-x^{2}+92x=2080$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+92x}{-1}=\frac{2080}{-1}$$

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

$$x^{2}+\frac{92}{-1}x=\frac{2080}{-1}$$

92 ni -1 ga bo'lish.

$$x^{2}-92x=\frac{2080}{-1}$$

2080 ni -1 ga bo'lish.

$$x^{2}-92x=-2080$$

-92 ni bo‘lish, x shartining koeffitsienti, 2 ga -46 olish uchun. Keyin, -46 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-92x+\left(-46\right)^{2}=-2080+\left(-46\right)^{2}$$

-46 kvadratini chiqarish.

$$x^{2}-92x+2116=-2080+2116$$

-2080 ni 2116 ga qo'shish.

$$x^{2}-92x+2116=36$$

x^{2}-92x+2116 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-46\right)^{2}=36$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-46\right)^{2}}=\sqrt{36}$$

Qisqartirish.

$$x-46=6 x-46=-6$$

46 ni tenglamaning ikkala tarafiga qo'shish.

$$x=52 x=40$$