left(68+2dright)(68+d)=144 eching

$$\left( 68+2d \right) (68+d) = 144$$

d uchun yechish

$$d=-70$$

$$d=-32$$

Kvadrat tenglamalaridan foydalanish qoidalari

68+2d ga 68+d ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4624+204d+2d^{2}=144$$

Ikkala tarafdan 144 ni ayirish.

$$4624+204d+2d^{2}-144=0$$

4480 olish uchun 4624 dan 144 ni ayirish.

$$4480+204d+2d^{2}=0$$

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.

$$2d^{2}+204d+4480=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 204 ni b va 4480 ni c bilan almashtiring.

$$d=\frac{-204±\sqrt{204^{2}-4\times 2\times 4480}}{2\times 2}$$

204 kvadratini chiqarish.

$$d=\frac{-204±\sqrt{41616-4\times 2\times 4480}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$d=\frac{-204±\sqrt{41616-8\times 4480}}{2\times 2}$$

-8 ni 4480 marotabaga ko'paytirish.

$$d=\frac{-204±\sqrt{41616-35840}}{2\times 2}$$

41616 ni -35840 ga qo'shish.

$$d=\frac{-204±\sqrt{5776}}{2\times 2}$$

5776 ning kvadrat ildizini chiqarish.

$$d=\frac{-204±76}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$d=\frac{-204±76}{4}$$

d=\frac{-204±76}{4} tenglamasini yeching, bunda ± musbat. -204 ni 76 ga qo'shish.

$$d=-\frac{128}{4}$$

-128 ni 4 ga bo'lish.

$$d=-32$$

d=\frac{-204±76}{4} tenglamasini yeching, bunda ± manfiy. -204 dan 76 ni ayirish.

$$d=-\frac{280}{4}$$

-280 ni 4 ga bo'lish.

$$d=-70$$

Tenglama yechildi.

$$d=-32 d=-70$$

Kvadratni yakunlash bo'yicha qadamlar

68+2d ga 68+d ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4624+204d+2d^{2}=144$$

Ikkala tarafdan 4624 ni ayirish.

$$204d+2d^{2}=144-4624$$

-4480 olish uchun 144 dan 4624 ni ayirish.

$$204d+2d^{2}=-4480$$

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

$$2d^{2}+204d=-4480$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2d^{2}+204d}{2}=-\frac{4480}{2}$$

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

$$d^{2}+\frac{204}{2}d=-\frac{4480}{2}$$

204 ni 2 ga bo'lish.

$$d^{2}+102d=-\frac{4480}{2}$$

-4480 ni 2 ga bo'lish.

$$d^{2}+102d=-2240$$

102 ni bo‘lish, x shartining koeffitsienti, 2 ga 51 olish uchun. Keyin, 51 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$d^{2}+102d+51^{2}=-2240+51^{2}$$

51 kvadratini chiqarish.

$$d^{2}+102d+2601=-2240+2601$$

-2240 ni 2601 ga qo'shish.

$$d^{2}+102d+2601=361$$

d^{2}+102d+2601 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(d+51\right)^{2}=361$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(d+51\right)^{2}}=\sqrt{361}$$

Qisqartirish.

$$d+51=19 d+51=-19$$

Tenglamaning ikkala tarafidan 51 ni ayirish.

$$d=-32 d=-70$$