4x*2x+3x=72 eching

$$4x \times 2x+3x=72$$

x uchun yechish

$$x = \frac{3 \sqrt{257} - 3}{16} \approx 2,818353664$$

$$x=\frac{-3\sqrt{257}-3}{16}\approx -3,193353664$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$4x^{2}\times 2+3x=72$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$8x^{2}+3x=72$$

Ikkala tarafdan 72 ni ayirish.

$$8x^{2}+3x-72=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, 3 ni b va -72 ni c bilan almashtiring.

$$x=\frac{-3±\sqrt{3^{2}-4\times 8\left(-72\right)}}{2\times 8}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\times 8\left(-72\right)}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9-32\left(-72\right)}}{2\times 8}$$

-32 ni -72 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+2304}}{2\times 8}$$

9 ni 2304 ga qo'shish.

$$x=\frac{-3±\sqrt{2313}}{2\times 8}$$

2313 ning kvadrat ildizini chiqarish.

$$x=\frac{-3±3\sqrt{257}}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{-3±3\sqrt{257}}{16}$$

x=\frac{-3±3\sqrt{257}}{16} tenglamasini yeching, bunda ± musbat. -3 ni 3\sqrt{257} ga qo'shish.

$$x=\frac{3\sqrt{257}-3}{16}$$

x=\frac{-3±3\sqrt{257}}{16} tenglamasini yeching, bunda ± manfiy. -3 dan 3\sqrt{257} ni ayirish.

$$x=\frac{-3\sqrt{257}-3}{16}$$

Tenglama yechildi.

$$x=\frac{3\sqrt{257}-3}{16} x=\frac{-3\sqrt{257}-3}{16}$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$4x^{2}\times 2+3x=72$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$8x^{2}+3x=72$$

Ikki tarafini 8 ga bo‘ling.

$$\frac{8x^{2}+3x}{8}=\frac{72}{8}$$

8 ga bo'lish 8 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{3}{8}x=\frac{72}{8}$$

72 ni 8 ga bo'lish.

$$x^{2}+\frac{3}{8}x=9$$

\frac{3}{8} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{16} olish uchun. Keyin, \frac{3}{16} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{3}{8}x+\left(\frac{3}{16}\right)^{2}=9+\left(\frac{3}{16}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{16} kvadratini chiqarish.

$$x^{2}+\frac{3}{8}x+\frac{9}{256}=9+\frac{9}{256}$$

9 ni \frac{9}{256} ga qo'shish.

$$x^{2}+\frac{3}{8}x+\frac{9}{256}=\frac{2313}{256}$$

x^{2}+\frac{3}{8}x+\frac{9}{256} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{16}\right)^{2}=\frac{2313}{256}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{16}\right)^{2}}=\sqrt{\frac{2313}{256}}$$

Qisqartirish.

$$x+\frac{3}{16}=\frac{3\sqrt{257}}{16} x+\frac{3}{16}=-\frac{3\sqrt{257}}{16}$$

Tenglamaning ikkala tarafidan \frac{3}{16} ni ayirish.

$$x=\frac{3\sqrt{257}-3}{16} x=\frac{-3\sqrt{257}-3}{16}$$