-2x^2+100x-800=0 eching

$$-2 { x }^{ 2 } +100x-800=0$$

x uchun yechish

$$x=10$$

$$x=40$$

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.

$$-2x^{2}+100x-800=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 100 ni b va -800 ni c bilan almashtiring.

$$x=\frac{-100±\sqrt{100^{2}-4\left(-2\right)\left(-800\right)}}{2\left(-2\right)}$$

100 kvadratini chiqarish.

$$x=\frac{-100±\sqrt{10000-4\left(-2\right)\left(-800\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-100±\sqrt{10000+8\left(-800\right)}}{2\left(-2\right)}$$

8 ni -800 marotabaga ko'paytirish.

$$x=\frac{-100±\sqrt{10000-6400}}{2\left(-2\right)}$$

10000 ni -6400 ga qo'shish.

$$x=\frac{-100±\sqrt{3600}}{2\left(-2\right)}$$

3600 ning kvadrat ildizini chiqarish.

$$x=\frac{-100±60}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-100±60}{-4}$$

x=\frac{-100±60}{-4} tenglamasini yeching, bunda ± musbat. -100 ni 60 ga qo'shish.

$$x=-\frac{40}{-4}$$

-40 ni -4 ga bo'lish.

$$x=10$$

x=\frac{-100±60}{-4} tenglamasini yeching, bunda ± manfiy. -100 dan 60 ni ayirish.

$$x=-\frac{160}{-4}$$

-160 ni -4 ga bo'lish.

$$x=40$$

Tenglama yechildi.

$$x=10 x=40$$

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.

$$-2x^{2}+100x-800=0$$

800 ni tenglamaning ikkala tarafiga qo'shish.

$$-2x^{2}+100x-800-\left(-800\right)=-\left(-800\right)$$

O‘zidan -800 ayirilsa 0 qoladi.

$$-2x^{2}+100x=-\left(-800\right)$$

0 dan -800 ni ayirish.

$$-2x^{2}+100x=800$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+100x}{-2}=\frac{800}{-2}$$

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

$$x^{2}+\frac{100}{-2}x=\frac{800}{-2}$$

100 ni -2 ga bo'lish.

$$x^{2}-50x=\frac{800}{-2}$$

800 ni -2 ga bo'lish.

$$x^{2}-50x=-400$$

-50 ni bo‘lish, x shartining koeffitsienti, 2 ga -25 olish uchun. Keyin, -25 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-50x+\left(-25\right)^{2}=-400+\left(-25\right)^{2}$$

-25 kvadratini chiqarish.

$$x^{2}-50x+625=-400+625$$

-400 ni 625 ga qo'shish.

$$x^{2}-50x+625=225$$

x^{2}-50x+625 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-25\right)^{2}=225$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-25\right)^{2}}=\sqrt{225}$$

Qisqartirish.

$$x-25=15 x-25=-15$$

25 ni tenglamaning ikkala tarafiga qo'shish.

$$x=40 x=10$$