960=(x+15)(x+5) eching

$$960 = ( x + 15 ) ( x + 5 )$$

x uchun yechish (complex solution)

$$x=\sqrt{985}-10\approx 21,384709653$$

$$x=-\left(\sqrt{985}+10\right)\approx -41,384709653$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+15 ga x+5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$960=x^{2}+20x+75$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+20x+75=960$$

Ikkala tarafdan 960 ni ayirish.

$$x^{2}+20x+75-960=0$$

-885 olish uchun 75 dan 960 ni ayirish.

$$x^{2}+20x-885=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 20 ni b va -885 ni c bilan almashtiring.

$$x=\frac{-20±\sqrt{20^{2}-4\left(-885\right)}}{2}$$

20 kvadratini chiqarish.

$$x=\frac{-20±\sqrt{400-4\left(-885\right)}}{2}$$

-4 ni -885 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400+3540}}{2}$$

400 ni 3540 ga qo'shish.

$$x=\frac{-20±\sqrt{3940}}{2}$$

3940 ning kvadrat ildizini chiqarish.

$$x=\frac{-20±2\sqrt{985}}{2}$$

x=\frac{-20±2\sqrt{985}}{2} tenglamasini yeching, bunda ± musbat. -20 ni 2\sqrt{985} ga qo'shish.

$$x=\frac{2\sqrt{985}-20}{2}$$

-20+2\sqrt{985} ni 2 ga bo'lish.

$$x=\sqrt{985}-10$$

x=\frac{-20±2\sqrt{985}}{2} tenglamasini yeching, bunda ± manfiy. -20 dan 2\sqrt{985} ni ayirish.

$$x=\frac{-2\sqrt{985}-20}{2}$$

-20-2\sqrt{985} ni 2 ga bo'lish.

$$x=-\sqrt{985}-10$$

Tenglama yechildi.

$$x=\sqrt{985}-10 x=-\sqrt{985}-10$$

Kvadratni yakunlash bo'yicha qadamlar

x+15 ga x+5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$960=x^{2}+20x+75$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+20x+75=960$$

Ikkala tarafdan 75 ni ayirish.

$$x^{2}+20x=960-75$$

885 olish uchun 960 dan 75 ni ayirish.

$$x^{2}+20x=885$$

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

$$x^{2}+20x+10^{2}=885+10^{2}$$

10 kvadratini chiqarish.

$$x^{2}+20x+100=885+100$$

885 ni 100 ga qo'shish.

$$x^{2}+20x+100=985$$

x^{2}+20x+100 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+10\right)^{2}=985$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{985}$$

Qisqartirish.

$$x+10=\sqrt{985} x+10=-\sqrt{985}$$

Tenglamaning ikkala tarafidan 10 ni ayirish.

$$x=\sqrt{985}-10 x=-\sqrt{985}-10$$

x uchun yechish

$$x=\sqrt{985}-10\approx 21,384709653$$

$$x=-\sqrt{985}-10\approx -41,384709653$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+15 ga x+5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$960=x^{2}+20x+75$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+20x+75=960$$

Ikkala tarafdan 960 ni ayirish.

$$x^{2}+20x+75-960=0$$

-885 olish uchun 75 dan 960 ni ayirish.

$$x^{2}+20x-885=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 20 ni b va -885 ni c bilan almashtiring.

$$x=\frac{-20±\sqrt{20^{2}-4\left(-885\right)}}{2}$$

20 kvadratini chiqarish.

$$x=\frac{-20±\sqrt{400-4\left(-885\right)}}{2}$$

-4 ni -885 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400+3540}}{2}$$

400 ni 3540 ga qo'shish.

$$x=\frac{-20±\sqrt{3940}}{2}$$

3940 ning kvadrat ildizini chiqarish.

$$x=\frac{-20±2\sqrt{985}}{2}$$

x=\frac{-20±2\sqrt{985}}{2} tenglamasini yeching, bunda ± musbat. -20 ni 2\sqrt{985} ga qo'shish.

$$x=\frac{2\sqrt{985}-20}{2}$$

-20+2\sqrt{985} ni 2 ga bo'lish.

$$x=\sqrt{985}-10$$

x=\frac{-20±2\sqrt{985}}{2} tenglamasini yeching, bunda ± manfiy. -20 dan 2\sqrt{985} ni ayirish.

$$x=\frac{-2\sqrt{985}-20}{2}$$

-20-2\sqrt{985} ni 2 ga bo'lish.

$$x=-\sqrt{985}-10$$

Tenglama yechildi.

$$x=\sqrt{985}-10 x=-\sqrt{985}-10$$

Kvadratni yakunlash bo'yicha qadamlar

x+15 ga x+5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$960=x^{2}+20x+75$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+20x+75=960$$

Ikkala tarafdan 75 ni ayirish.

$$x^{2}+20x=960-75$$

885 olish uchun 960 dan 75 ni ayirish.

$$x^{2}+20x=885$$

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

$$x^{2}+20x+10^{2}=885+10^{2}$$

10 kvadratini chiqarish.

$$x^{2}+20x+100=885+100$$

885 ni 100 ga qo'shish.

$$x^{2}+20x+100=985$$

x^{2}+20x+100 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+10\right)^{2}=985$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{985}$$

Qisqartirish.

$$x+10=\sqrt{985} x+10=-\sqrt{985}$$

Tenglamaning ikkala tarafidan 10 ni ayirish.

$$x=\sqrt{985}-10 x=-\sqrt{985}-10$$