(1)=60(x+3)(x-2 eching

$$(1)=60(x+3)(x-2$$

x uchun yechish

$$x=\frac{\sqrt{1410}}{15}-\frac{1}{2}\approx 2,003331114$$

$$x=-\frac{\sqrt{1410}}{15}-\frac{1}{2}\approx -3,003331114$$

Kvadrat tenglamalaridan foydalanish qoidalari

60 ga x+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1=\left(60x+180\right)\left(x-2\right)$$

60x+180 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$1=60x^{2}+60x-360$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$60x^{2}+60x-360=1$$

Ikkala tarafdan 1 ni ayirish.

$$60x^{2}+60x-360-1=0$$

-361 olish uchun -360 dan 1 ni ayirish.

$$60x^{2}+60x-361=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 60 ni a, 60 ni b va -361 ni c bilan almashtiring.

$$x=\frac{-60±\sqrt{60^{2}-4\times 60\left(-361\right)}}{2\times 60}$$

60 kvadratini chiqarish.

$$x=\frac{-60±\sqrt{3600-4\times 60\left(-361\right)}}{2\times 60}$$

-4 ni 60 marotabaga ko'paytirish.

$$x=\frac{-60±\sqrt{3600-240\left(-361\right)}}{2\times 60}$$

-240 ni -361 marotabaga ko'paytirish.

$$x=\frac{-60±\sqrt{3600+86640}}{2\times 60}$$

3600 ni 86640 ga qo'shish.

$$x=\frac{-60±\sqrt{90240}}{2\times 60}$$

90240 ning kvadrat ildizini chiqarish.

$$x=\frac{-60±8\sqrt{1410}}{2\times 60}$$

2 ni 60 marotabaga ko'paytirish.

$$x=\frac{-60±8\sqrt{1410}}{120}$$

x=\frac{-60±8\sqrt{1410}}{120} tenglamasini yeching, bunda ± musbat. -60 ni 8\sqrt{1410} ga qo'shish.

$$x=\frac{8\sqrt{1410}-60}{120}$$

-60+8\sqrt{1410} ni 120 ga bo'lish.

$$x=\frac{\sqrt{1410}}{15}-\frac{1}{2}$$

x=\frac{-60±8\sqrt{1410}}{120} tenglamasini yeching, bunda ± manfiy. -60 dan 8\sqrt{1410} ni ayirish.

$$x=\frac{-8\sqrt{1410}-60}{120}$$

-60-8\sqrt{1410} ni 120 ga bo'lish.

$$x=-\frac{\sqrt{1410}}{15}-\frac{1}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{1410}}{15}-\frac{1}{2} x=-\frac{\sqrt{1410}}{15}-\frac{1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

60 ga x+3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1=\left(60x+180\right)\left(x-2\right)$$

60x+180 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$1=60x^{2}+60x-360$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$60x^{2}+60x-360=1$$

360 ni ikki tarafga qo’shing.

$$60x^{2}+60x=1+360$$

361 olish uchun 1 va 360'ni qo'shing.

$$60x^{2}+60x=361$$

Ikki tarafini 60 ga bo‘ling.

$$\frac{60x^{2}+60x}{60}=\frac{361}{60}$$

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

$$x^{2}+\frac{60}{60}x=\frac{361}{60}$$

60 ni 60 ga bo'lish.

$$x^{2}+x=\frac{361}{60}$$

1 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{2} olish uchun. Keyin, \frac{1}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=\frac{361}{60}+\left(\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{2} kvadratini chiqarish.

$$x^{2}+x+\frac{1}{4}=\frac{361}{60}+\frac{1}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{361}{60} ni \frac{1}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+x+\frac{1}{4}=\frac{94}{15}$$

x^{2}+x+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{94}{15}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{94}{15}}$$

Qisqartirish.

$$x+\frac{1}{2}=\frac{\sqrt{1410}}{15} x+\frac{1}{2}=-\frac{\sqrt{1410}}{15}$$

Tenglamaning ikkala tarafidan \frac{1}{2} ni ayirish.

$$x=\frac{\sqrt{1410}}{15}-\frac{1}{2} x=-\frac{\sqrt{1410}}{15}-\frac{1}{2}$$