(x-10)(-2x+80)=450 eching

$$( x - 10 ) ( - 2 x + 80 ) = 450$$

x uchun yechish

$$x=25$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-10 ga -2x+80 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-2x^{2}+100x-800=450$$

Ikkala tarafdan 450 ni ayirish.

$$-2x^{2}+100x-800-450=0$$

-1250 olish uchun -800 dan 450 ni ayirish.

$$-2x^{2}+100x-1250=0$$

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 -1250 ni c bilan almashtiring.

$$x=\frac{-100±\sqrt{100^{2}-4\left(-2\right)\left(-1250\right)}}{2\left(-2\right)}$$

100 kvadratini chiqarish.

$$x=\frac{-100±\sqrt{10000-4\left(-2\right)\left(-1250\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-100±\sqrt{10000+8\left(-1250\right)}}{2\left(-2\right)}$$

8 ni -1250 marotabaga ko'paytirish.

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

10000 ni -10000 ga qo'shish.

$$x=\frac{-100±\sqrt{0}}{2\left(-2\right)}$$

0 ning kvadrat ildizini chiqarish.

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

2 ni -2 marotabaga ko'paytirish.

$$x=-\frac{100}{-4}$$

-100 ni -4 ga bo'lish.

$$x=25$$

Kvadratni yakunlash bo'yicha qadamlar

x-10 ga -2x+80 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$-2x^{2}+100x-800=450$$

800 ni ikki tarafga qo’shing.

$$-2x^{2}+100x=450+800$$

1250 olish uchun 450 va 800'ni qo'shing.

$$-2x^{2}+100x=1250$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+100x}{-2}=\frac{1250}{-2}$$

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

$$x^{2}+\frac{100}{-2}x=\frac{1250}{-2}$$

100 ni -2 ga bo'lish.

$$x^{2}-50x=\frac{1250}{-2}$$

1250 ni -2 ga bo'lish.

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

-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.

$$x^{2}-50x+\left(-25\right)^{2}=-625+\left(-25\right)^{2}$$

-25 kvadratini chiqarish.

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

-625 ni 625 ga qo'shish.

$$x^{2}-50x+625=0$$

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.

$$\left(x-25\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-25\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$x-25=0 x-25=0$$

25 ni tenglamaning ikkala tarafiga qo'shish.

$$x=25 x=25$$

Tenglama yechildi. Yechimlar bir xil.

$$x=25$$