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Solve using the quadratic formula.\newline7x2+9x+1=07x^2 + 9x + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____

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Q. Solve using the quadratic formula.\newline7x2+9x+1=07x^2 + 9x + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____
  1. Identify Coefficients: To solve the quadratic equation 7x2+9x+1=07x^2 + 9x + 1 = 0 using the quadratic formula, we first need to identify the coefficients aa, bb, and cc from the equation, where aa is the coefficient of x2x^2, bb is the coefficient of xx, and cc is the constant term.\newlineIn this equation, a=7a = 7, aa00, and aa11.
  2. Quadratic Formula: The quadratic formula is given by x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. We will use this formula to find the values of xx.
  3. Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac.\newlineDiscriminant = 92−4(7)(1)=81−28=539^2 - 4(7)(1) = 81 - 28 = 53.
  4. Find Solutions: Since the discriminant is positive, we will have two real and distinct solutions for xx. Now we will use the quadratic formula to find the two solutions for xx.
  5. First Solution: First solution using the positive square root:\newlinex=−9+532×7x = \frac{-9 + \sqrt{53}}{2 \times 7}\newlinex=−9+5314x = \frac{-9 + \sqrt{53}}{14}
  6. Second Solution: Second solution using the negative square root:\newlinex=−9−532×7x = \frac{-9 - \sqrt{53}}{2 \times 7}\newlinex=−9−5314x = \frac{-9 - \sqrt{53}}{14}
  7. Simplify Solutions: Now we can simplify the solutions if possible. However, since 53\sqrt{53} cannot be simplified to a simpler radical and the fractions cannot be reduced further, we will leave the solutions in this form or convert them to decimal form rounded to the nearest hundredth.\newlineFirst solution as a decimal:\newlinex≈(−9+7.28)/14x \approx (-9 + 7.28) / 14\newlinex≈−1.72/14x \approx -1.72 / 14\newline$x \approx \(-0\).\(12\)
  8. Simplify Solutions: Now we can simplify the solutions if possible. However, since \(\sqrt{53}\) cannot be simplified to a simpler radical and the fractions cannot be reduced further, we will leave the solutions in this form or convert them to decimal form rounded to the nearest hundredth.\(\newline\)First solution as a decimal:\(\newline\)\(x \approx (-9 + 7.28) / 14\)\(\newline\)\(x \approx -1.72 / 14\)\(\newline\)\(x \approx -0.12\)Second solution as a decimal:\(\newline\)\(x \approx (-9 - 7.28) / 14\)\(\newline\)\(x \approx -16.28 / 14\)\(\newline\)\(x \approx -1.16\)

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