5062=R(R+200) eching

$$5062 = R ( R + 200 )$$

R uchun yechish

$$R=\sqrt{15062}-100\approx 22,727340067$$

$$R=-\sqrt{15062}-100\approx -222,727340067$$

Kvadrat tenglamalaridan foydalanish qoidalari

R ga R+200 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5062=R^{2}+200R$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$R^{2}+200R=5062$$

Ikkala tarafdan 5062 ni ayirish.

$$R^{2}+200R-5062=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 200 ni b va -5062 ni c bilan almashtiring.

$$R=\frac{-200±\sqrt{200^{2}-4\left(-5062\right)}}{2}$$

200 kvadratini chiqarish.

$$R=\frac{-200±\sqrt{40000-4\left(-5062\right)}}{2}$$

-4 ni -5062 marotabaga ko'paytirish.

$$R=\frac{-200±\sqrt{40000+20248}}{2}$$

40000 ni 20248 ga qo'shish.

$$R=\frac{-200±\sqrt{60248}}{2}$$

60248 ning kvadrat ildizini chiqarish.

$$R=\frac{-200±2\sqrt{15062}}{2}$$

R=\frac{-200±2\sqrt{15062}}{2} tenglamasini yeching, bunda ± musbat. -200 ni 2\sqrt{15062} ga qo'shish.

$$R=\frac{2\sqrt{15062}-200}{2}$$

-200+2\sqrt{15062} ni 2 ga bo'lish.

$$R=\sqrt{15062}-100$$

R=\frac{-200±2\sqrt{15062}}{2} tenglamasini yeching, bunda ± manfiy. -200 dan 2\sqrt{15062} ni ayirish.

$$R=\frac{-2\sqrt{15062}-200}{2}$$

-200-2\sqrt{15062} ni 2 ga bo'lish.

$$R=-\sqrt{15062}-100$$

Tenglama yechildi.

$$R=\sqrt{15062}-100 R=-\sqrt{15062}-100$$

Kvadratni yakunlash bo'yicha qadamlar

R ga R+200 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5062=R^{2}+200R$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$R^{2}+200R=5062$$

200 ni bo‘lish, x shartining koeffitsienti, 2 ga 100 olish uchun. Keyin, 100 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$R^{2}+200R+100^{2}=5062+100^{2}$$

100 kvadratini chiqarish.

$$R^{2}+200R+10000=5062+10000$$

5062 ni 10000 ga qo'shish.

$$R^{2}+200R+10000=15062$$

R^{2}+200R+10000 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(R+100\right)^{2}=15062$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(R+100\right)^{2}}=\sqrt{15062}$$

Qisqartirish.

$$R+100=\sqrt{15062} R+100=-\sqrt{15062}$$

Tenglamaning ikkala tarafidan 100 ni ayirish.

$$R=\sqrt{15062}-100 R=-\sqrt{15062}-100$$