25-100x^2=0 eching

$$25-100 { x }^{ 2 } =0$$

x uchun yechish

$$x=\frac{1}{2}=0,5$$

$$x=-\frac{1}{2}=-0,5$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 25 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-100x^{2}=-25$$

Ikki tarafini -100 ga bo‘ling.

$$x^{2}=\frac{-25}{-100}$$

\frac{-25}{-100} ulushini -25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

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.

$$-100x^{2}+25=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -100 ni a, 0 ni b va 25 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-100\right)\times 25}}{2\left(-100\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-100\right)\times 25}}{2\left(-100\right)}$$

-4 ni -100 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{400\times 25}}{2\left(-100\right)}$$

400 ni 25 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{10000}}{2\left(-100\right)}$$

10000 ning kvadrat ildizini chiqarish.

$$x=\frac{0±100}{2\left(-100\right)}$$

2 ni -100 marotabaga ko'paytirish.

$$x=\frac{0±100}{-200}$$

x=\frac{0±100}{-200} tenglamasini yeching, bunda ± musbat. \frac{100}{-200} ulushini 100 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x=\frac{0±100}{-200} tenglamasini yeching, bunda ± manfiy. \frac{-100}{-200} ulushini 100 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

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