0=40-49x^2 eching

$$0=40-49 { x }^{ 2 }$$

x uchun yechish

$$x=\frac{2\sqrt{10}}{7}\approx 0,903507903$$

$$x=-\frac{2\sqrt{10}}{7}\approx -0,903507903$$

Kvadrat ildizini topish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$40-49x^{2}=0$$

Ikkala tarafdan 40 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-49x^{2}=-40$$

Ikki tarafini -49 ga bo‘ling.

$$x^{2}=\frac{-40}{-49}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-40}{-49} kasrini \frac{40}{49} ga soddalashtirish mumkin.

$$x^{2}=\frac{40}{49}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{2\sqrt{10}}{7} x=-\frac{2\sqrt{10}}{7}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$40-49x^{2}=0$$

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.

$$-49x^{2}+40=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -49 ni a, 0 ni b va 40 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-49\right)\times 40}}{2\left(-49\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-49\right)\times 40}}{2\left(-49\right)}$$

-4 ni -49 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{196\times 40}}{2\left(-49\right)}$$

196 ni 40 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{7840}}{2\left(-49\right)}$$

7840 ning kvadrat ildizini chiqarish.

$$x=\frac{0±28\sqrt{10}}{2\left(-49\right)}$$

2 ni -49 marotabaga ko'paytirish.

$$x=\frac{0±28\sqrt{10}}{-98}$$

x=\frac{0±28\sqrt{10}}{-98} tenglamasini yeching, bunda ± musbat.

$$x=-\frac{2\sqrt{10}}{7}$$

x=\frac{0±28\sqrt{10}}{-98} tenglamasini yeching, bunda ± manfiy.

$$x=\frac{2\sqrt{10}}{7}$$

Tenglama yechildi.

$$x=-\frac{2\sqrt{10}}{7} x=\frac{2\sqrt{10}}{7}$$