25=2x^2-8x+6 eching

$$25 = 2 x ^ { 2 } - 8 x + 6$$

x uchun yechish

$$x=\frac{3\sqrt{6}}{2}+2\approx 5,674234614$$

$$x=-\frac{3\sqrt{6}}{2}+2\approx -1,674234614$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2x^{2}-8x+6=25$$

Ikkala tarafdan 25 ni ayirish.

$$2x^{2}-8x+6-25=0$$

-19 olish uchun 6 dan 25 ni ayirish.

$$2x^{2}-8x-19=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -8 ni b va -19 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\left(-19\right)}}{2\times 2}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\left(-19\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-8\left(-19\right)}}{2\times 2}$$

-8 ni -19 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+152}}{2\times 2}$$

64 ni 152 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{216}}{2\times 2}$$

216 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±6\sqrt{6}}{2\times 2}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±6\sqrt{6}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{8±6\sqrt{6}}{4}$$

x=\frac{8±6\sqrt{6}}{4} tenglamasini yeching, bunda ± musbat. 8 ni 6\sqrt{6} ga qo'shish.

$$x=\frac{6\sqrt{6}+8}{4}$$

6\sqrt{6}+8 ni 4 ga bo'lish.

$$x=\frac{3\sqrt{6}}{2}+2$$

x=\frac{8±6\sqrt{6}}{4} tenglamasini yeching, bunda ± manfiy. 8 dan 6\sqrt{6} ni ayirish.

$$x=\frac{8-6\sqrt{6}}{4}$$

8-6\sqrt{6} ni 4 ga bo'lish.

$$x=-\frac{3\sqrt{6}}{2}+2$$

Tenglama yechildi.

$$x=\frac{3\sqrt{6}}{2}+2 x=-\frac{3\sqrt{6}}{2}+2$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2x^{2}-8x+6=25$$

Ikkala tarafdan 6 ni ayirish.

$$2x^{2}-8x=25-6$$

19 olish uchun 25 dan 6 ni ayirish.

$$2x^{2}-8x=19$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-8x}{2}=\frac{19}{2}$$

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

$$x^{2}+\left(-\frac{8}{2}\right)x=\frac{19}{2}$$

-8 ni 2 ga bo'lish.

$$x^{2}-4x=\frac{19}{2}$$

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

$$x^{2}-4x+\left(-2\right)^{2}=\frac{19}{2}+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=\frac{19}{2}+4$$

\frac{19}{2} ni 4 ga qo'shish.

$$x^{2}-4x+4=\frac{27}{2}$$

x^{2}-4x+4 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-2\right)^{2}=\frac{27}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{\frac{27}{2}}$$

Qisqartirish.

$$x-2=\frac{3\sqrt{6}}{2} x-2=-\frac{3\sqrt{6}}{2}$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3\sqrt{6}}{2}+2 x=-\frac{3\sqrt{6}}{2}+2$$