5x^2+75x=0 eching

$$5 x ^ { 2 } + 75 x = 0$$

x uchun yechish

$$x=-15$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(5x+75\right)=0$$

Tenglamani yechish uchun x=0 va 5x+75=0 ni yeching.

$$x=0 x=-15$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$5x^{2}+75x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, 75 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-75±\sqrt{75^{2}}}{2\times 5}$$

75^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-75±75}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{-75±75}{10}$$

x=\frac{-75±75}{10} tenglamasini yeching, bunda ± musbat. -75 ni 75 ga qo'shish.

$$x=\frac{0}{10}$$

0 ni 10 ga bo'lish.

$$x=0$$

x=\frac{-75±75}{10} tenglamasini yeching, bunda ± manfiy. -75 dan 75 ni ayirish.

$$x=-\frac{150}{10}$$

-150 ni 10 ga bo'lish.

$$x=-15$$

Tenglama yechildi.

$$x=0 x=-15$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$5x^{2}+75x=0$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}+75x}{5}=\frac{0}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{75}{5}x=\frac{0}{5}$$

75 ni 5 ga bo'lish.

$$x^{2}+15x=\frac{0}{5}$$

0 ni 5 ga bo'lish.

$$x^{2}+15x=0$$

15 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{15}{2} olish uchun. Keyin, \frac{15}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+15x+\left(\frac{15}{2}\right)^{2}=\left(\frac{15}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{15}{2} kvadratini chiqarish.

$$x^{2}+15x+\frac{225}{4}=\frac{225}{4}$$

x^{2}+15x+\frac{225}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{15}{2}\right)^{2}=\frac{225}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{15}{2}\right)^{2}}=\sqrt{\frac{225}{4}}$$

Qisqartirish.

$$x+\frac{15}{2}=\frac{15}{2} x+\frac{15}{2}=-\frac{15}{2}$$

Tenglamaning ikkala tarafidan \frac{15}{2} ni ayirish.

$$x=0 x=-15$$