2x^2-7500+300x=0 eching

$$2 { x }^{ 2 } -7500+300x=0$$

x uchun yechish

$$x=25\sqrt{15}-75\approx 21,824583655$$

$$x=-25\sqrt{15}-75\approx -171,824583655$$

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.

$$2x^{2}+300x-7500=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 300 ni b va -7500 ni c bilan almashtiring.

$$x=\frac{-300±\sqrt{300^{2}-4\times 2\left(-7500\right)}}{2\times 2}$$

300 kvadratini chiqarish.

$$x=\frac{-300±\sqrt{90000-4\times 2\left(-7500\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-300±\sqrt{90000-8\left(-7500\right)}}{2\times 2}$$

-8 ni -7500 marotabaga ko'paytirish.

$$x=\frac{-300±\sqrt{90000+60000}}{2\times 2}$$

90000 ni 60000 ga qo'shish.

$$x=\frac{-300±\sqrt{150000}}{2\times 2}$$

150000 ning kvadrat ildizini chiqarish.

$$x=\frac{-300±100\sqrt{15}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-300±100\sqrt{15}}{4}$$

x=\frac{-300±100\sqrt{15}}{4} tenglamasini yeching, bunda ± musbat. -300 ni 100\sqrt{15} ga qo'shish.

$$x=\frac{100\sqrt{15}-300}{4}$$

-300+100\sqrt{15} ni 4 ga bo'lish.

$$x=25\sqrt{15}-75$$

x=\frac{-300±100\sqrt{15}}{4} tenglamasini yeching, bunda ± manfiy. -300 dan 100\sqrt{15} ni ayirish.

$$x=\frac{-100\sqrt{15}-300}{4}$$

-300-100\sqrt{15} ni 4 ga bo'lish.

$$x=-25\sqrt{15}-75$$

Tenglama yechildi.

$$x=25\sqrt{15}-75 x=-25\sqrt{15}-75$$

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.

$$2x^{2}+300x-7500=0$$

7500 ni tenglamaning ikkala tarafiga qo'shish.

$$2x^{2}+300x-7500-\left(-7500\right)=-\left(-7500\right)$$

O‘zidan -7500 ayirilsa 0 qoladi.

$$2x^{2}+300x=-\left(-7500\right)$$

0 dan -7500 ni ayirish.

$$2x^{2}+300x=7500$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+300x}{2}=\frac{7500}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{300}{2}x=\frac{7500}{2}$$

300 ni 2 ga bo'lish.

$$x^{2}+150x=\frac{7500}{2}$$

7500 ni 2 ga bo'lish.

$$x^{2}+150x=3750$$

150 ni bo‘lish, x shartining koeffitsienti, 2 ga 75 olish uchun. Keyin, 75 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+150x+75^{2}=3750+75^{2}$$

75 kvadratini chiqarish.

$$x^{2}+150x+5625=3750+5625$$

3750 ni 5625 ga qo'shish.

$$x^{2}+150x+5625=9375$$

x^{2}+150x+5625 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+75\right)^{2}=9375$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+75\right)^{2}}=\sqrt{9375}$$

Qisqartirish.

$$x+75=25\sqrt{15} x+75=-25\sqrt{15}$$

Tenglamaning ikkala tarafidan 75 ni ayirish.

$$x=25\sqrt{15}-75 x=-25\sqrt{15}-75$$