x^2+4x=9(3/4) eching

$$x ^ { 2 } + 4 x = 9 ( 3 / 4 )$$

x uchun yechish

$$x=\frac{\sqrt{43}}{2}-2\approx 1,278719262$$

$$x=-\frac{\sqrt{43}}{2}-2\approx -5,278719262$$

Kvadrat tenglamalaridan foydalanish qoidalari

\frac{27}{4} hosil qilish uchun 9 va \frac{3}{4} ni ko'paytirish.

$$x^{2}+4x=\frac{27}{4}$$

Ikkala tarafdan \frac{27}{4} ni ayirish.

$$x^{2}+4x-\frac{27}{4}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 4 ni b va -\frac{27}{4} ni c bilan almashtiring.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-\frac{27}{4}\right)}}{2}$$

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\left(-\frac{27}{4}\right)}}{2}$$

-4 ni -\frac{27}{4} marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+27}}{2}$$

16 ni 27 ga qo'shish.

$$x=\frac{-4±\sqrt{43}}{2}$$

x=\frac{-4±\sqrt{43}}{2} tenglamasini yeching, bunda ± musbat. -4 ni \sqrt{43} ga qo'shish.

$$x=\frac{\sqrt{43}-4}{2}$$

-4+\sqrt{43} ni 2 ga bo'lish.

$$x=\frac{\sqrt{43}}{2}-2$$

x=\frac{-4±\sqrt{43}}{2} tenglamasini yeching, bunda ± manfiy. -4 dan \sqrt{43} ni ayirish.

$$x=\frac{-\sqrt{43}-4}{2}$$

-4-\sqrt{43} ni 2 ga bo'lish.

$$x=-\frac{\sqrt{43}}{2}-2$$

Tenglama yechildi.

$$x=\frac{\sqrt{43}}{2}-2 x=-\frac{\sqrt{43}}{2}-2$$

Kvadratni yakunlash bo'yicha qadamlar

\frac{27}{4} hosil qilish uchun 9 va \frac{3}{4} ni ko'paytirish.

$$x^{2}+4x=\frac{27}{4}$$

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

$$x^{2}+4x+2^{2}=\frac{27}{4}+2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=\frac{27}{4}+4$$

\frac{27}{4} ni 4 ga qo'shish.

$$x^{2}+4x+4=\frac{43}{4}$$

x^{2}+4x+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.

$$\left(x+2\right)^{2}=\frac{43}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{\frac{43}{4}}$$

Qisqartirish.

$$x+2=\frac{\sqrt{43}}{2} x+2=-\frac{\sqrt{43}}{2}$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=\frac{\sqrt{43}}{2}-2 x=-\frac{\sqrt{43}}{2}-2$$