Kelly Bird
11/15/2023 · Middle School
2) \( 2 x^{2}+6 x-7=0 \)
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Tutor-Verified Answer
Step-by-step Solution
Чтобы решить уравнение \( 2x^{2} + 6x - 7 = 0 \), мы можем использовать формулу квадратного уравнения:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
где \( a = 2 \), \( b = 6 \), \( c = -7 \).
Сначала найдем дискриминант \( D \):
\[
D = b^2 - 4ac = 6^2 - 4 \cdot 2 \cdot (-7) = 36 + 56 = 92
\]
Теперь подставим значения в формулу:
\[
x = \frac{-6 \pm \sqrt{92}}{2 \cdot 2}
\]
Упростим \( \sqrt{92} \):
\[
\sqrt{92} = \sqrt{4 \cdot 23} = 2\sqrt{23}
\]
Теперь подставим это значение обратно в формулу:
\[
x = \frac{-6 \pm 2\sqrt{23}}{4}
\]
Упростим дробь:
\[
x = \frac{-3 \pm \sqrt{23}}{2}
\]
Таким образом, у нас есть два решения:
\[
x_1 = \frac{-3 + \sqrt{23}}{2}, \quad x_2 = \frac{-3 - \sqrt{23}}{2}
\]
Quick Answer
Решения уравнения \( 2x^{2} + 6x - 7 = 0 \) — \( x_1 = \frac{-3 + \sqrt{23}}{2} \) и \( x_2 = \frac{-3 - \sqrt{23}}{2} \).
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