400x^2-4800x+18000=22500-7500x+625x^2 eching

$$400 { x }^{ 2 } -4800x+18000=22500-7500x+625 { x }^{ 2 }$$

x uchun yechish

$$x=2$$

$$x=10$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 22500 ni ayirish.

$$400x^{2}-4800x+18000-22500=-7500x+625x^{2}$$

-4500 olish uchun 18000 dan 22500 ni ayirish.

$$400x^{2}-4800x-4500=-7500x+625x^{2}$$

7500x ni ikki tarafga qo’shing.

$$400x^{2}-4800x-4500+7500x=625x^{2}$$

2700x ni olish uchun -4800x va 7500x ni birlashtirish.

$$400x^{2}+2700x-4500=625x^{2}$$

Ikkala tarafdan 625x^{2} ni ayirish.

$$400x^{2}+2700x-4500-625x^{2}=0$$

-225x^{2} ni olish uchun 400x^{2} va -625x^{2} ni birlashtirish.

$$-225x^{2}+2700x-4500=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -225 ni a, 2700 ni b va -4500 ni c bilan almashtiring.

$$x=\frac{-2700±\sqrt{2700^{2}-4\left(-225\right)\left(-4500\right)}}{2\left(-225\right)}$$

2700 kvadratini chiqarish.

$$x=\frac{-2700±\sqrt{7290000-4\left(-225\right)\left(-4500\right)}}{2\left(-225\right)}$$

-4 ni -225 marotabaga ko'paytirish.

$$x=\frac{-2700±\sqrt{7290000+900\left(-4500\right)}}{2\left(-225\right)}$$

900 ni -4500 marotabaga ko'paytirish.

$$x=\frac{-2700±\sqrt{7290000-4050000}}{2\left(-225\right)}$$

7290000 ni -4050000 ga qo'shish.

$$x=\frac{-2700±\sqrt{3240000}}{2\left(-225\right)}$$

3240000 ning kvadrat ildizini chiqarish.

$$x=\frac{-2700±1800}{2\left(-225\right)}$$

2 ni -225 marotabaga ko'paytirish.

$$x=\frac{-2700±1800}{-450}$$

x=\frac{-2700±1800}{-450} tenglamasini yeching, bunda ± musbat. -2700 ni 1800 ga qo'shish.

$$x=-\frac{900}{-450}$$

-900 ni -450 ga bo'lish.

$$x=2$$

x=\frac{-2700±1800}{-450} tenglamasini yeching, bunda ± manfiy. -2700 dan 1800 ni ayirish.

$$x=-\frac{4500}{-450}$$

-4500 ni -450 ga bo'lish.

$$x=10$$

Tenglama yechildi.

$$x=2 x=10$$

Kvadratni yakunlash bo'yicha qadamlar

7500x ni ikki tarafga qo’shing.

$$400x^{2}-4800x+18000+7500x=22500+625x^{2}$$

2700x ni olish uchun -4800x va 7500x ni birlashtirish.

$$400x^{2}+2700x+18000=22500+625x^{2}$$

Ikkala tarafdan 625x^{2} ni ayirish.

$$400x^{2}+2700x+18000-625x^{2}=22500$$

-225x^{2} ni olish uchun 400x^{2} va -625x^{2} ni birlashtirish.

$$-225x^{2}+2700x+18000=22500$$

Ikkala tarafdan 18000 ni ayirish.

$$-225x^{2}+2700x=22500-18000$$

4500 olish uchun 22500 dan 18000 ni ayirish.

$$-225x^{2}+2700x=4500$$

Ikki tarafini -225 ga bo‘ling.

$$\frac{-225x^{2}+2700x}{-225}=\frac{4500}{-225}$$

-225 ga bo'lish -225 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{2700}{-225}x=\frac{4500}{-225}$$

2700 ni -225 ga bo'lish.

$$x^{2}-12x=\frac{4500}{-225}$$

4500 ni -225 ga bo'lish.

$$x^{2}-12x=-20$$

-12 ni bo‘lish, x shartining koeffitsienti, 2 ga -6 olish uchun. Keyin, -6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-12x+\left(-6\right)^{2}=-20+\left(-6\right)^{2}$$

-6 kvadratini chiqarish.

$$x^{2}-12x+36=-20+36$$

-20 ni 36 ga qo'shish.

$$x^{2}-12x+36=16$$

x^{2}-12x+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-6\right)^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{16}$$

Qisqartirish.

$$x-6=4 x-6=-4$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$x=10 x=2$$