5=1/2250x^2+1/250left(x+02right)^2 eching

$$5 = \frac{ 1 }{ 2 } 250 { x }^{ 2 } + \frac{ 1 }{ 2 } 50 { \left(x+02 \right) }^{ 2 }$$

x uchun yechish

$$x=\frac{\sqrt{30}}{30}\approx 0,182574186$$

$$x=-\frac{\sqrt{30}}{30}\approx -0,182574186$$

Kvadrat ildizini topish bo'yicha qadamlar

125 hosil qilish uchun \frac{1}{2} va 250 ni ko'paytirish.

$$5=125x^{2}+\frac{1}{2}\times 50\left(x+0\times 2\right)^{2}$$

25 hosil qilish uchun \frac{1}{2} va 50 ni ko'paytirish.

$$5=125x^{2}+25\left(x+0\times 2\right)^{2}$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$5=125x^{2}+25\left(x+0\right)^{2}$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$5=125x^{2}+25x^{2}$$

150x^{2} ni olish uchun 125x^{2} va 25x^{2} ni birlashtirish.

$$5=150x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$150x^{2}=5$$

Ikki tarafini 150 ga bo‘ling.

$$x^{2}=\frac{5}{150}$$

\frac{5}{150} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{1}{30}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{30}}{30} x=-\frac{\sqrt{30}}{30}$$

Kvadrat tenglamalaridan foydalanish qoidalari

125 hosil qilish uchun \frac{1}{2} va 250 ni ko'paytirish.

$$5=125x^{2}+\frac{1}{2}\times 50\left(x+0\times 2\right)^{2}$$

25 hosil qilish uchun \frac{1}{2} va 50 ni ko'paytirish.

$$5=125x^{2}+25\left(x+0\times 2\right)^{2}$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$5=125x^{2}+25\left(x+0\right)^{2}$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$5=125x^{2}+25x^{2}$$

150x^{2} ni olish uchun 125x^{2} va 25x^{2} ni birlashtirish.

$$5=150x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$150x^{2}=5$$

Ikkala tarafdan 5 ni ayirish.

$$150x^{2}-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 150 ni a, 0 ni b va -5 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 150\left(-5\right)}}{2\times 150}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 150\left(-5\right)}}{2\times 150}$$

-4 ni 150 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-600\left(-5\right)}}{2\times 150}$$

-600 ni -5 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{3000}}{2\times 150}$$

3000 ning kvadrat ildizini chiqarish.

$$x=\frac{0±10\sqrt{30}}{2\times 150}$$

2 ni 150 marotabaga ko'paytirish.

$$x=\frac{0±10\sqrt{30}}{300}$$

x=\frac{0±10\sqrt{30}}{300} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{30}}{30}$$

x=\frac{0±10\sqrt{30}}{300} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{30}}{30}$$

Tenglama yechildi.

$$x=\frac{\sqrt{30}}{30} x=-\frac{\sqrt{30}}{30}$$