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To solve the quadratic equation \(9x^2 - 7x - 2 = 0\), we can use the quadratic formula:
The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this equation, \(a = 9\), \(b = -7\), and \(c = -2\).
Substitute these values into the formula:
\[ x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(9)(-2)}}{2(9)} \]
Simplify:
\[ x = \frac{7 \pm \sqrt{49 + 72}}{18} \]
\[ x = \frac{7 \pm \sqrt{121}}{18} \]
\[ x = \frac{7 \pm 11}{18} \]
Now we have two possible solutions:
1. When using the plus sign:
\[ x = \frac{7 + 11}{18} = \frac{18}{18} = 1 \]
2. When using the minus sign:
\[ x = \frac{7 - 11}{18} = \frac{-4}{18} = -\frac{2}{9} \]
Therefore, the solutions to the equation \(9x^2 - 7x - 2 = 0\) are \(x = 1\) and \(x = -\frac{2}{9}\).
The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this equation, \(a = 9\), \(b = -7\), and \(c = -2\).
Substitute these values into the formula:
\[ x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(9)(-2)}}{2(9)} \]
Simplify:
\[ x = \frac{7 \pm \sqrt{49 + 72}}{18} \]
\[ x = \frac{7 \pm \sqrt{121}}{18} \]
\[ x = \frac{7 \pm 11}{18} \]
Now we have two possible solutions:
1. When using the plus sign:
\[ x = \frac{7 + 11}{18} = \frac{18}{18} = 1 \]
2. When using the minus sign:
\[ x = \frac{7 - 11}{18} = \frac{-4}{18} = -\frac{2}{9} \]
Therefore, the solutions to the equation \(9x^2 - 7x - 2 = 0\) are \(x = 1\) and \(x = -\frac{2}{9}\).
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11 декабря 2024 12:33
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