(40-m)(20+2m)=120 eching

$$( 40 - m ) ( 20 + 2 m ) = 120$$

m uchun yechish

$$m=\sqrt{565}+15\approx 38,769728648$$

$$m=15-\sqrt{565}\approx -8,769728648$$

Kvadrat tenglamalaridan foydalanish qoidalari

40-m ga 20+2m ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$800+60m-2m^{2}=120$$

Ikkala tarafdan 120 ni ayirish.

$$800+60m-2m^{2}-120=0$$

680 olish uchun 800 dan 120 ni ayirish.

$$680+60m-2m^{2}=0$$

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.

$$-2m^{2}+60m+680=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 60 ni b va 680 ni c bilan almashtiring.

$$m=\frac{-60±\sqrt{60^{2}-4\left(-2\right)\times 680}}{2\left(-2\right)}$$

60 kvadratini chiqarish.

$$m=\frac{-60±\sqrt{3600-4\left(-2\right)\times 680}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$m=\frac{-60±\sqrt{3600+8\times 680}}{2\left(-2\right)}$$

8 ni 680 marotabaga ko'paytirish.

$$m=\frac{-60±\sqrt{3600+5440}}{2\left(-2\right)}$$

3600 ni 5440 ga qo'shish.

$$m=\frac{-60±\sqrt{9040}}{2\left(-2\right)}$$

9040 ning kvadrat ildizini chiqarish.

$$m=\frac{-60±4\sqrt{565}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$m=\frac{-60±4\sqrt{565}}{-4}$$

m=\frac{-60±4\sqrt{565}}{-4} tenglamasini yeching, bunda ± musbat. -60 ni 4\sqrt{565} ga qo'shish.

$$m=\frac{4\sqrt{565}-60}{-4}$$

-60+4\sqrt{565} ni -4 ga bo'lish.

$$m=15-\sqrt{565}$$

m=\frac{-60±4\sqrt{565}}{-4} tenglamasini yeching, bunda ± manfiy. -60 dan 4\sqrt{565} ni ayirish.

$$m=\frac{-4\sqrt{565}-60}{-4}$$

-60-4\sqrt{565} ni -4 ga bo'lish.

$$m=\sqrt{565}+15$$

Tenglama yechildi.

$$m=15-\sqrt{565} m=\sqrt{565}+15$$

Kvadratni yakunlash bo'yicha qadamlar

40-m ga 20+2m ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$800+60m-2m^{2}=120$$

Ikkala tarafdan 800 ni ayirish.

$$60m-2m^{2}=120-800$$

-680 olish uchun 120 dan 800 ni ayirish.

$$60m-2m^{2}=-680$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-2m^{2}+60m=-680$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2m^{2}+60m}{-2}=-\frac{680}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$m^{2}+\frac{60}{-2}m=-\frac{680}{-2}$$

60 ni -2 ga bo'lish.

$$m^{2}-30m=-\frac{680}{-2}$$

-680 ni -2 ga bo'lish.

$$m^{2}-30m=340$$

-30 ni bo‘lish, x shartining koeffitsienti, 2 ga -15 olish uchun. Keyin, -15 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$m^{2}-30m+\left(-15\right)^{2}=340+\left(-15\right)^{2}$$

-15 kvadratini chiqarish.

$$m^{2}-30m+225=340+225$$

340 ni 225 ga qo'shish.

$$m^{2}-30m+225=565$$

m^{2}-30m+225 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(m-15\right)^{2}=565$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m-15\right)^{2}}=\sqrt{565}$$

Qisqartirish.

$$m-15=\sqrt{565} m-15=-\sqrt{565}$$

15 ni tenglamaning ikkala tarafiga qo'shish.

$$m=\sqrt{565}+15 m=15-\sqrt{565}$$