45=90/4+x^2 eching

$$45 = \frac { 90 } { 4 } + x ^ { 2 }$$

x uchun yechish

$$x = \frac{3 \sqrt{10}}{2} \approx 4,74341649$$

$$x = -\frac{3 \sqrt{10}}{2} \approx -4,74341649$$

Kvadrat ildizini topish bo'yicha qadamlar

\frac{90}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$45=\frac{45}{2}+x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{45}{2}+x^{2}=45$$

Ikkala tarafdan \frac{45}{2} ni ayirish.

$$x^{2}=45-\frac{45}{2}$$

\frac{45}{2} olish uchun 45 dan \frac{45}{2} ni ayirish.

$$x^{2}=\frac{45}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{3\sqrt{10}}{2} x=-\frac{3\sqrt{10}}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\frac{90}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$45=\frac{45}{2}+x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{45}{2}+x^{2}=45$$

Ikkala tarafdan 45 ni ayirish.

$$\frac{45}{2}+x^{2}-45=0$$

-\frac{45}{2} olish uchun \frac{45}{2} dan 45 ni ayirish.

$$-\frac{45}{2}+x^{2}=0$$

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.

$$x^{2}-\frac{45}{2}=0$$

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{45}{2} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{45}{2}\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{45}{2}\right)}}{2}$$

-4 ni -\frac{45}{2} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{90}}{2}$$

90 ning kvadrat ildizini chiqarish.

$$x=\frac{0±3\sqrt{10}}{2}$$

x=\frac{0±3\sqrt{10}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\frac{3\sqrt{10}}{2}$$

x=\frac{0±3\sqrt{10}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{3\sqrt{10}}{2}$$

Tenglama yechildi.

$$x=\frac{3\sqrt{10}}{2} x=-\frac{3\sqrt{10}}{2}$$