x^2-360x-3240=0 eching

$$x ^ { 2 } - 360 x - 3240 = 0$$

x uchun yechish

$$x=18\sqrt{110}+180\approx 368,785592671$$

$$x=180-18\sqrt{110}\approx -8,785592671$$

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.

$$x^{2}-360x-3240=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -360 ni b va -3240 ni c bilan almashtiring.

$$x=\frac{-\left(-360\right)±\sqrt{\left(-360\right)^{2}-4\left(-3240\right)}}{2}$$

-360 kvadratini chiqarish.

$$x=\frac{-\left(-360\right)±\sqrt{129600-4\left(-3240\right)}}{2}$$

-4 ni -3240 marotabaga ko'paytirish.

$$x=\frac{-\left(-360\right)±\sqrt{129600+12960}}{2}$$

129600 ni 12960 ga qo'shish.

$$x=\frac{-\left(-360\right)±\sqrt{142560}}{2}$$

142560 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-360\right)±36\sqrt{110}}{2}$$

-360 ning teskarisi 360 ga teng.

$$x=\frac{360±36\sqrt{110}}{2}$$

x=\frac{360±36\sqrt{110}}{2} tenglamasini yeching, bunda ± musbat. 360 ni 36\sqrt{110} ga qo'shish.

$$x=\frac{36\sqrt{110}+360}{2}$$

360+36\sqrt{110} ni 2 ga bo'lish.

$$x=18\sqrt{110}+180$$

x=\frac{360±36\sqrt{110}}{2} tenglamasini yeching, bunda ± manfiy. 360 dan 36\sqrt{110} ni ayirish.

$$x=\frac{360-36\sqrt{110}}{2}$$

360-36\sqrt{110} ni 2 ga bo'lish.

$$x=180-18\sqrt{110}$$

Tenglama yechildi.

$$x=18\sqrt{110}+180 x=180-18\sqrt{110}$$

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.

$$x^{2}-360x-3240=0$$

3240 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-360x-3240-\left(-3240\right)=-\left(-3240\right)$$

O‘zidan -3240 ayirilsa 0 qoladi.

$$x^{2}-360x=-\left(-3240\right)$$

0 dan -3240 ni ayirish.

$$x^{2}-360x=3240$$

-360 ni bo‘lish, x shartining koeffitsienti, 2 ga -180 olish uchun. Keyin, -180 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-360x+\left(-180\right)^{2}=3240+\left(-180\right)^{2}$$

-180 kvadratini chiqarish.

$$x^{2}-360x+32400=3240+32400$$

3240 ni 32400 ga qo'shish.

$$x^{2}-360x+32400=35640$$

x^{2}-360x+32400 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-180\right)^{2}=35640$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-180\right)^{2}}=\sqrt{35640}$$

Qisqartirish.

$$x-180=18\sqrt{110} x-180=-18\sqrt{110}$$

180 ni tenglamaning ikkala tarafiga qo'shish.

$$x=18\sqrt{110}+180 x=180-18\sqrt{110}$$