(40-x)(20+2x)=1250 eching

$$(40-x)(20+2x)=1250$$

x uchun yechish

$$x=15$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$800+60x-2x^{2}=1250$$

Ikkala tarafdan 1250 ni ayirish.

$$800+60x-2x^{2}-1250=0$$

-450 olish uchun 800 dan 1250 ni ayirish.

$$-450+60x-2x^{2}=0$$

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.

$$-2x^{2}+60x-450=0$$

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 -450 ni c bilan almashtiring.

$$x=\frac{-60±\sqrt{60^{2}-4\left(-2\right)\left(-450\right)}}{2\left(-2\right)}$$

60 kvadratini chiqarish.

$$x=\frac{-60±\sqrt{3600-4\left(-2\right)\left(-450\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-60±\sqrt{3600+8\left(-450\right)}}{2\left(-2\right)}$$

8 ni -450 marotabaga ko'paytirish.

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

3600 ni -3600 ga qo'shish.

$$x=\frac{-60±\sqrt{0}}{2\left(-2\right)}$$

0 ning kvadrat ildizini chiqarish.

$$x=-\frac{60}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=-\frac{60}{-4}$$

-60 ni -4 ga bo'lish.

$$x=15$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$800+60x-2x^{2}=1250$$

Ikkala tarafdan 800 ni ayirish.

$$60x-2x^{2}=1250-800$$

450 olish uchun 1250 dan 800 ni ayirish.

$$60x-2x^{2}=450$$

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

$$-2x^{2}+60x=450$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+60x}{-2}=\frac{450}{-2}$$

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

$$x^{2}+\frac{60}{-2}x=\frac{450}{-2}$$

60 ni -2 ga bo'lish.

$$x^{2}-30x=\frac{450}{-2}$$

450 ni -2 ga bo'lish.

$$x^{2}-30x=-225$$

-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.

$$x^{2}-30x+\left(-15\right)^{2}=-225+\left(-15\right)^{2}$$

-15 kvadratini chiqarish.

$$x^{2}-30x+225=-225+225$$

-225 ni 225 ga qo'shish.

$$x^{2}-30x+225=0$$

x^{2}-30x+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.

$$\left(x-15\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-15\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$x-15=0 x-15=0$$

15 ni tenglamaning ikkala tarafiga qo'shish.

$$x=15 x=15$$

Tenglama yechildi. Yechimlar bir xil.

$$x=15$$