(40+x)*(3/2x+60)=6420 eching

$$( 40 + x ) \times ( \frac { 3 } { 2 } x + 60 ) = 6420$$

x uchun yechish

$$x=2\sqrt{1070}-40\approx 25,421708935$$

$$x=-2\sqrt{1070}-40\approx -105,421708935$$

Kvadrat tenglamalaridan foydalanish qoidalari

40+x ga \frac{3}{2}x+60 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$120x+2400+\frac{3}{2}x^{2}=6420$$

Ikkala tarafdan 6420 ni ayirish.

$$120x+2400+\frac{3}{2}x^{2}-6420=0$$

-4020 olish uchun 2400 dan 6420 ni ayirish.

$$120x-4020+\frac{3}{2}x^{2}=0$$

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.

$$\frac{3}{2}x^{2}+120x-4020=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{3}{2} ni a, 120 ni b va -4020 ni c bilan almashtiring.

$$x=\frac{-120±\sqrt{120^{2}-4\times \frac{3}{2}\left(-4020\right)}}{2\times \frac{3}{2}}$$

120 kvadratini chiqarish.

$$x=\frac{-120±\sqrt{14400-4\times \frac{3}{2}\left(-4020\right)}}{2\times \frac{3}{2}}$$

-4 ni \frac{3}{2} marotabaga ko'paytirish.

$$x=\frac{-120±\sqrt{14400-6\left(-4020\right)}}{2\times \frac{3}{2}}$$

-6 ni -4020 marotabaga ko'paytirish.

$$x=\frac{-120±\sqrt{14400+24120}}{2\times \frac{3}{2}}$$

14400 ni 24120 ga qo'shish.

$$x=\frac{-120±\sqrt{38520}}{2\times \frac{3}{2}}$$

38520 ning kvadrat ildizini chiqarish.

$$x=\frac{-120±6\sqrt{1070}}{2\times \frac{3}{2}}$$

2 ni \frac{3}{2} marotabaga ko'paytirish.

$$x=\frac{-120±6\sqrt{1070}}{3}$$

x=\frac{-120±6\sqrt{1070}}{3} tenglamasini yeching, bunda ± musbat. -120 ni 6\sqrt{1070} ga qo'shish.

$$x=\frac{6\sqrt{1070}-120}{3}$$

-120+6\sqrt{1070} ni 3 ga bo'lish.

$$x=2\sqrt{1070}-40$$

x=\frac{-120±6\sqrt{1070}}{3} tenglamasini yeching, bunda ± manfiy. -120 dan 6\sqrt{1070} ni ayirish.

$$x=\frac{-6\sqrt{1070}-120}{3}$$

-120-6\sqrt{1070} ni 3 ga bo'lish.

$$x=-2\sqrt{1070}-40$$

Tenglama yechildi.

$$x=2\sqrt{1070}-40 x=-2\sqrt{1070}-40$$

Kvadratni yakunlash bo'yicha qadamlar

40+x ga \frac{3}{2}x+60 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$120x+2400+\frac{3}{2}x^{2}=6420$$

Ikkala tarafdan 2400 ni ayirish.

$$120x+\frac{3}{2}x^{2}=6420-2400$$

4020 olish uchun 6420 dan 2400 ni ayirish.

$$120x+\frac{3}{2}x^{2}=4020$$

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

$$\frac{3}{2}x^{2}+120x=4020$$

Tenglamaning ikki tarafini \frac{3}{2} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

$$\frac{\frac{3}{2}x^{2}+120x}{\frac{3}{2}}=\frac{4020}{\frac{3}{2}}$$

\frac{3}{2} ga bo'lish \frac{3}{2} ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{120}{\frac{3}{2}}x=\frac{4020}{\frac{3}{2}}$$

120 ni \frac{3}{2} ga bo'lish 120 ga k'paytirish \frac{3}{2} ga qaytarish.

$$x^{2}+80x=\frac{4020}{\frac{3}{2}}$$

4020 ni \frac{3}{2} ga bo'lish 4020 ga k'paytirish \frac{3}{2} ga qaytarish.

$$x^{2}+80x=2680$$

80 ni bo‘lish, x shartining koeffitsienti, 2 ga 40 olish uchun. Keyin, 40 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+80x+40^{2}=2680+40^{2}$$

40 kvadratini chiqarish.

$$x^{2}+80x+1600=2680+1600$$

2680 ni 1600 ga qo'shish.

$$x^{2}+80x+1600=4280$$

x^{2}+80x+1600 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+40\right)^{2}=4280$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+40\right)^{2}}=\sqrt{4280}$$

Qisqartirish.

$$x+40=2\sqrt{1070} x+40=-2\sqrt{1070}$$

Tenglamaning ikkala tarafidan 40 ni ayirish.

$$x=2\sqrt{1070}-40 x=-2\sqrt{1070}-40$$