4x^2-25=0 eching

$$4 x ^ { 2 } - 25 = 0$$

x uchun yechish

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

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

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: 4x^{2}-25. 4x^{2}-25 ni \left(2x\right)^{2}-5^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-5\right)\left(2x+5\right)=0$$

Tenglamani yechish uchun 2x-5=0 va 2x+5=0 ni yeching.

$$x=\frac{5}{2} x=-\frac{5}{2}$$

Kvadrat ildizini topish bo'yicha qadamlar

25 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$4x^{2}=25$$

Ikki tarafini 4 ga bo‘ling.

$$x^{2}=\frac{25}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{5}{2} x=-\frac{5}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$4x^{2}-25=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 0 ni b va -25 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-25\right)}}{2\times 4}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 4\left(-25\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-16\left(-25\right)}}{2\times 4}$$

-16 ni -25 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{400}}{2\times 4}$$

400 ning kvadrat ildizini chiqarish.

$$x=\frac{0±20}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{0±20}{8}$$

x=\frac{0±20}{8} tenglamasini yeching, bunda ± musbat. \frac{20}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{5}{2}$$

x=\frac{0±20}{8} tenglamasini yeching, bunda ± manfiy. \frac{-20}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{5}{2}$$

Tenglama yechildi.

$$x=\frac{5}{2} x=-\frac{5}{2}$$