x^2-7x-30=x eching

$$x ^ { 2 } - 7 x - 30 = x$$

x uchun yechish

$$x=\sqrt{46}+4\approx 10,782329983$$

$$x=4-\sqrt{46}\approx -2,782329983$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan x ni ayirish.

$$x^{2}-7x-30-x=0$$

-8x ni olish uchun -7x va -x ni birlashtirish.

$$x^{2}-8x-30=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -8 ni b va -30 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-30\right)}}{2}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-30\right)}}{2}$$

-4 ni -30 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+120}}{2}$$

64 ni 120 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{184}}{2}$$

184 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±2\sqrt{46}}{2}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±2\sqrt{46}}{2}$$

x=\frac{8±2\sqrt{46}}{2} tenglamasini yeching, bunda ± musbat. 8 ni 2\sqrt{46} ga qo'shish.

$$x=\frac{2\sqrt{46}+8}{2}$$

8+2\sqrt{46} ni 2 ga bo'lish.

$$x=\sqrt{46}+4$$

x=\frac{8±2\sqrt{46}}{2} tenglamasini yeching, bunda ± manfiy. 8 dan 2\sqrt{46} ni ayirish.

$$x=\frac{8-2\sqrt{46}}{2}$$

8-2\sqrt{46} ni 2 ga bo'lish.

$$x=4-\sqrt{46}$$

Tenglama yechildi.

$$x=\sqrt{46}+4 x=4-\sqrt{46}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan x ni ayirish.

$$x^{2}-7x-30-x=0$$

-8x ni olish uchun -7x va -x ni birlashtirish.

$$x^{2}-8x-30=0$$

30 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}-8x=30$$

-8 ni bo‘lish, x shartining koeffitsienti, 2 ga -4 olish uchun. Keyin, -4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-8x+\left(-4\right)^{2}=30+\left(-4\right)^{2}$$

-4 kvadratini chiqarish.

$$x^{2}-8x+16=30+16$$

30 ni 16 ga qo'shish.

$$x^{2}-8x+16=46$$

x^{2}-8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-4\right)^{2}=46$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{46}$$

Qisqartirish.

$$x-4=\sqrt{46} x-4=-\sqrt{46}$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{46}+4 x=4-\sqrt{46}$$