(10-x)(8+2x)=90 eching

$$( 10 - x ) ( 8 + 2 x ) = 90$$

x uchun yechish

$$x=1$$

$$x=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

10-x ga 8+2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$80+12x-2x^{2}=90$$

Ikkala tarafdan 90 ni ayirish.

$$80+12x-2x^{2}-90=0$$

-10 olish uchun 80 dan 90 ni ayirish.

$$-10+12x-2x^{2}=0$$

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.

$$-2x^{2}+12x-10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 12 ni b va -10 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-2\right)\left(-10\right)}}{2\left(-2\right)}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\left(-2\right)\left(-10\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+8\left(-10\right)}}{2\left(-2\right)}$$

8 ni -10 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-80}}{2\left(-2\right)}$$

144 ni -80 ga qo'shish.

$$x=\frac{-12±\sqrt{64}}{2\left(-2\right)}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±8}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-12±8}{-4}$$

x=\frac{-12±8}{-4} tenglamasini yeching, bunda ± musbat. -12 ni 8 ga qo'shish.

$$x=-\frac{4}{-4}$$

-4 ni -4 ga bo'lish.

$$x=1$$

x=\frac{-12±8}{-4} tenglamasini yeching, bunda ± manfiy. -12 dan 8 ni ayirish.

$$x=-\frac{20}{-4}$$

-20 ni -4 ga bo'lish.

$$x=5$$

Tenglama yechildi.

$$x=1 x=5$$

Kvadratni yakunlash bo'yicha qadamlar

10-x ga 8+2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$80+12x-2x^{2}=90$$

Ikkala tarafdan 80 ni ayirish.

$$12x-2x^{2}=90-80$$

10 olish uchun 90 dan 80 ni ayirish.

$$12x-2x^{2}=10$$

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

$$-2x^{2}+12x=10$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+12x}{-2}=\frac{10}{-2}$$

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

$$x^{2}+\frac{12}{-2}x=\frac{10}{-2}$$

12 ni -2 ga bo'lish.

$$x^{2}-6x=\frac{10}{-2}$$

10 ni -2 ga bo'lish.

$$x^{2}-6x=-5$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-6x+\left(-3\right)^{2}=-5+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=-5+9$$

-5 ni 9 ga qo'shish.

$$x^{2}-6x+9=4$$

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-3\right)^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{4}$$

Qisqartirish.

$$x-3=2 x-3=-2$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=5 x=1$$