-20387=1018t+t^2 eching

$$- 20387 = 1018 t + t ^ { 2 }$$

t uchun yechish

$$t=\sqrt{238694}-509\approx -20,436800403$$

$$t=-\sqrt{238694}-509\approx -997,563199597$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1018t+t^{2}=-20387$$

20387 ni ikki tarafga qo’shing.

$$1018t+t^{2}+20387=0$$

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.

$$t^{2}+1018t+20387=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 1018 ni b va 20387 ni c bilan almashtiring.

$$t=\frac{-1018±\sqrt{1018^{2}-4\times 20387}}{2}$$

1018 kvadratini chiqarish.

$$t=\frac{-1018±\sqrt{1036324-4\times 20387}}{2}$$

-4 ni 20387 marotabaga ko'paytirish.

$$t=\frac{-1018±\sqrt{1036324-81548}}{2}$$

1036324 ni -81548 ga qo'shish.

$$t=\frac{-1018±\sqrt{954776}}{2}$$

954776 ning kvadrat ildizini chiqarish.

$$t=\frac{-1018±2\sqrt{238694}}{2}$$

t=\frac{-1018±2\sqrt{238694}}{2} tenglamasini yeching, bunda ± musbat. -1018 ni 2\sqrt{238694} ga qo'shish.

$$t=\frac{2\sqrt{238694}-1018}{2}$$

-1018+2\sqrt{238694} ni 2 ga bo'lish.

$$t=\sqrt{238694}-509$$

t=\frac{-1018±2\sqrt{238694}}{2} tenglamasini yeching, bunda ± manfiy. -1018 dan 2\sqrt{238694} ni ayirish.

$$t=\frac{-2\sqrt{238694}-1018}{2}$$

-1018-2\sqrt{238694} ni 2 ga bo'lish.

$$t=-\sqrt{238694}-509$$

Tenglama yechildi.

$$t=\sqrt{238694}-509 t=-\sqrt{238694}-509$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1018t+t^{2}=-20387$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$t^{2}+1018t=-20387$$

1018 ni bo‘lish, x shartining koeffitsienti, 2 ga 509 olish uchun. Keyin, 509 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}+1018t+509^{2}=-20387+509^{2}$$

509 kvadratini chiqarish.

$$t^{2}+1018t+259081=-20387+259081$$

-20387 ni 259081 ga qo'shish.

$$t^{2}+1018t+259081=238694$$

t^{2}+1018t+259081 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t+509\right)^{2}=238694$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t+509\right)^{2}}=\sqrt{238694}$$

Qisqartirish.

$$t+509=\sqrt{238694} t+509=-\sqrt{238694}$$

Tenglamaning ikkala tarafidan 509 ni ayirish.

$$t=\sqrt{238694}-509 t=-\sqrt{238694}-509$$