Questions: Find the real solutions, if any, of the equation. Use the quadratic formula. x^2+7x+7=0

Transcript text: Find the real solutions, if any, of the equation. Use the quadratic formula. \[ x^{2}+7 x+7=0 \]

Solution

Solution Steps

Step 1: Identify the coefficients

The coefficients are \(a = 1\), \(b = 7\), and \(c = 7\).

Step 2: Calculate the discriminant

The discriminant, \(b^2 - 4ac\), is calculated as \(b^2 - 4 \cdot 1 \cdot 7 = 21\).

Step 3: Determine the nature of the roots

Since the discriminant is greater than 0, the equation has two distinct real roots.

Step 4: Calculate the roots using the quadratic formula

The roots are calculated using the formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Substituting the values, we get \(x_1 = (-1.21+0j)\) and \(x_2 = (-5.79+0j)\).

Final Answer:

The roots of the equation \(ax^2 + bx + c = 0\) are \(x_1 = (-1.21+0j)\) and \(x_2 = (-5.79+0j)\).

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