2=4(x^2-7/4) eching

$$2=4( { x }^{ 2 } - \frac{ 7 }{ 4 } )$$

x uchun yechish

$$x = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1,5$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 4 ga bo‘ling.

$$\frac{2}{4}=x^{2}-\frac{7}{4}$$

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}=x^{2}-\frac{7}{4}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-\frac{7}{4}=\frac{1}{2}$$

Ikkala tarafdan \frac{1}{2} ni ayirish.

$$x^{2}-\frac{7}{4}-\frac{1}{2}=0$$

-\frac{9}{4} olish uchun -\frac{7}{4} dan \frac{1}{2} ni ayirish.

$$x^{2}-\frac{9}{4}=0$$

Ikkala tarafini 4 ga ko‘paytiring.

$$4x^{2}-9=0$$

Hisoblang: 4x^{2}-9. 4x^{2}-9 ni \left(2x\right)^{2}-3^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-3\right)\left(2x+3\right)=0$$

Tenglamani yechish uchun 2x-3=0 va 2x+3=0 ni yeching.

$$x=\frac{3}{2} x=-\frac{3}{2}$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 4 ga bo‘ling.

$$\frac{2}{4}=x^{2}-\frac{7}{4}$$

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}=x^{2}-\frac{7}{4}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-\frac{7}{4}=\frac{1}{2}$$

\frac{7}{4} ni ikki tarafga qo’shing.

$$x^{2}=\frac{1}{2}+\frac{7}{4}$$

\frac{9}{4} olish uchun \frac{1}{2} va \frac{7}{4}'ni qo'shing.

$$x^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{3}{2} x=-\frac{3}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 4 ga bo‘ling.

$$\frac{2}{4}=x^{2}-\frac{7}{4}$$

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}=x^{2}-\frac{7}{4}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-\frac{7}{4}=\frac{1}{2}$$

Ikkala tarafdan \frac{1}{2} ni ayirish.

$$x^{2}-\frac{7}{4}-\frac{1}{2}=0$$

-\frac{9}{4} olish uchun -\frac{7}{4} dan \frac{1}{2} ni ayirish.

$$x^{2}-\frac{9}{4}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -\frac{9}{4} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{4}\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{9}{4}\right)}}{2}$$

-4 ni -\frac{9}{4} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{9}}{2}$$

9 ning kvadrat ildizini chiqarish.

$$x=\frac{0±3}{2}$$

x=\frac{0±3}{2} tenglamasini yeching, bunda ± musbat. 3 ni 2 ga bo'lish.

$$x=\frac{3}{2}$$

x=\frac{0±3}{2} tenglamasini yeching, bunda ± manfiy. -3 ni 2 ga bo'lish.

$$x=-\frac{3}{2}$$

Tenglama yechildi.

$$x=\frac{3}{2} x=-\frac{3}{2}$$