75*18=(75+x)(18-x) eching

$$75 \times 18 = ( 75 + x ) ( 18 - x )$$

x uchun yechish

$$x=-57$$

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

1350 hosil qilish uchun 75 va 18 ni ko'paytirish.

$$1350=\left(75+x\right)\left(18-x\right)$$

75+x ga 18-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$1350=1350-57x-x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1350-57x-x^{2}=1350$$

Ikkala tarafdan 1350 ni ayirish.

$$1350-57x-x^{2}-1350=0$$

0 olish uchun 1350 dan 1350 ni ayirish.

$$-57x-x^{2}=0$$

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.

$$-x^{2}-57x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -57 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-57\right)±\sqrt{\left(-57\right)^{2}}}{2\left(-1\right)}$$

\left(-57\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-57\right)±57}{2\left(-1\right)}$$

-57 ning teskarisi 57 ga teng.

$$x=\frac{57±57}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{57±57}{-2}$$

x=\frac{57±57}{-2} tenglamasini yeching, bunda ± musbat. 57 ni 57 ga qo'shish.

$$x=\frac{114}{-2}$$

114 ni -2 ga bo'lish.

$$x=-57$$

x=\frac{57±57}{-2} tenglamasini yeching, bunda ± manfiy. 57 dan 57 ni ayirish.

$$x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-57 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

1350 hosil qilish uchun 75 va 18 ni ko'paytirish.

$$1350=\left(75+x\right)\left(18-x\right)$$

75+x ga 18-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$1350=1350-57x-x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1350-57x-x^{2}=1350$$

Ikkala tarafdan 1350 ni ayirish.

$$-57x-x^{2}=1350-1350$$

0 olish uchun 1350 dan 1350 ni ayirish.

$$-57x-x^{2}=0$$

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

$$-x^{2}-57x=0$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-57x}{-1}=\frac{0}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{57}{-1}\right)x=\frac{0}{-1}$$

-57 ni -1 ga bo'lish.

$$x^{2}+57x=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

$$x^{2}+57x=0$$

57 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{57}{2} olish uchun. Keyin, \frac{57}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+57x+\left(\frac{57}{2}\right)^{2}=\left(\frac{57}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{57}{2} kvadratini chiqarish.

$$x^{2}+57x+\frac{3249}{4}=\frac{3249}{4}$$

x^{2}+57x+\frac{3249}{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.

$$\left(x+\frac{57}{2}\right)^{2}=\frac{3249}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{57}{2}\right)^{2}}=\sqrt{\frac{3249}{4}}$$

Qisqartirish.

$$x+\frac{57}{2}=\frac{57}{2} x+\frac{57}{2}=-\frac{57}{2}$$

Tenglamaning ikkala tarafidan \frac{57}{2} ni ayirish.

$$x=0 x=-57$$