0=60x^2-600x+1000 eching

$$0=60 { x }^{ 2 } -600x+1000$$

x uchun yechish

$$x=\frac{5\sqrt{3}}{3}+5\approx 7,886751346$$

$$x=-\frac{5\sqrt{3}}{3}+5\approx 2,113248654$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$60x^{2}-600x+1000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 60 ni a, -600 ni b va 1000 ni c bilan almashtiring.

$$x=\frac{-\left(-600\right)±\sqrt{\left(-600\right)^{2}-4\times 60\times 1000}}{2\times 60}$$

-600 kvadratini chiqarish.

$$x=\frac{-\left(-600\right)±\sqrt{360000-4\times 60\times 1000}}{2\times 60}$$

-4 ni 60 marotabaga ko'paytirish.

$$x=\frac{-\left(-600\right)±\sqrt{360000-240\times 1000}}{2\times 60}$$

-240 ni 1000 marotabaga ko'paytirish.

$$x=\frac{-\left(-600\right)±\sqrt{360000-240000}}{2\times 60}$$

360000 ni -240000 ga qo'shish.

$$x=\frac{-\left(-600\right)±\sqrt{120000}}{2\times 60}$$

120000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-600\right)±200\sqrt{3}}{2\times 60}$$

-600 ning teskarisi 600 ga teng.

$$x=\frac{600±200\sqrt{3}}{2\times 60}$$

2 ni 60 marotabaga ko'paytirish.

$$x=\frac{600±200\sqrt{3}}{120}$$

x=\frac{600±200\sqrt{3}}{120} tenglamasini yeching, bunda ± musbat. 600 ni 200\sqrt{3} ga qo'shish.

$$x=\frac{200\sqrt{3}+600}{120}$$

600+200\sqrt{3} ni 120 ga bo'lish.

$$x=\frac{5\sqrt{3}}{3}+5$$

x=\frac{600±200\sqrt{3}}{120} tenglamasini yeching, bunda ± manfiy. 600 dan 200\sqrt{3} ni ayirish.

$$x=\frac{600-200\sqrt{3}}{120}$$

600-200\sqrt{3} ni 120 ga bo'lish.

$$x=-\frac{5\sqrt{3}}{3}+5$$

Tenglama yechildi.

$$x=\frac{5\sqrt{3}}{3}+5 x=-\frac{5\sqrt{3}}{3}+5$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$60x^{2}-600x+1000=0$$

Ikkala tarafdan 1000 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$60x^{2}-600x=-1000$$

Ikki tarafini 60 ga bo‘ling.

$$\frac{60x^{2}-600x}{60}=-\frac{1000}{60}$$

60 ga bo'lish 60 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{600}{60}\right)x=-\frac{1000}{60}$$

-600 ni 60 ga bo'lish.

$$x^{2}-10x=-\frac{1000}{60}$$

\frac{-1000}{60} ulushini 20 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-10x=-\frac{50}{3}$$

-10 ni bo‘lish, x shartining koeffitsienti, 2 ga -5 olish uchun. Keyin, -5 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-10x+\left(-5\right)^{2}=-\frac{50}{3}+\left(-5\right)^{2}$$

-5 kvadratini chiqarish.

$$x^{2}-10x+25=-\frac{50}{3}+25$$

-\frac{50}{3} ni 25 ga qo'shish.

$$x^{2}-10x+25=\frac{25}{3}$$

x^{2}-10x+25 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-5\right)^{2}=\frac{25}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{\frac{25}{3}}$$

Qisqartirish.

$$x-5=\frac{5\sqrt{3}}{3} x-5=-\frac{5\sqrt{3}}{3}$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{5\sqrt{3}}{3}+5 x=-\frac{5\sqrt{3}}{3}+5$$