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

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. \[ x^{2}+7 x+7=0 \]
failed

Solution

failed
failed

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 \(x_2 = (-5.79+0j)\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
an objective indication of disease that is measurable by health care personnel
failedAnswered
Graph two full periods of the function. y=5 sin (5x+20)-1
failedAnswered
Which of the following is true about the transportation of substances across the lipid region of the cell membrane? Choose 1 answer: A Small nonpolar molecules can freely dissolve across the lipid region of the cell membrane. (B) Gases such as N2, O2, and CO2 require embedded transport proteins to dissolve across the lipid region of the cell membrane. (C) Polysaccharides can freely dissolve across the lipid region of the cell membrane. D Ions can freely dissolve across the lipid region of the cell membrane.
failedAnswered
Simplify. [ frac3(3 x^2+16 x+22)(3 x^2+20 x+32) ]
failedAnswered
Mr. Olson is a 65-year-old man who has come to the clinic for a complete physical checkup. He has no health complaints, and his physical examination is negative except for a few minor changes associated with aging. During the interview, he tells you that he is gay and has had the same partner for five years. On further questioning, he reveals that he has had numerous sex partners during his lifetime. He says, "I was wondering if I should be tested for HIV," and "Mike, that's my partner, says I ought to get a flu shot and maybe a hepatitis shot. What do you think?" What is one important nursing intervention for today?