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Solve using the quadratic formula.\newline9g2+g9=09g^2 + g - 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineg=g = _____ or g=g = _____

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Q. Solve using the quadratic formula.\newline9g2+g9=09g^2 + g - 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineg=g = _____ or g=g = _____
  1. Quadratic Formula Explanation: The quadratic formula is given by g=b±b24ac2ag = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation in the form of ax2+bx+c=0ax^2 + bx + c = 0. For the equation 9g2+g9=09g^2 + g - 9 = 0, a=9a = 9, b=1b = 1, and c=9c = -9.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b24acb^2 - 4ac. For our equation, the discriminant is 124(9)(9)=1+324=3251^2 - 4(9)(-9) = 1 + 324 = 325.
  3. Plug Values into Formula: Now, plug the values of aa, bb, and the discriminant into the quadratic formula to find the two possible values for gg.\newlineg=1±3252×9g = \frac{-1 \pm \sqrt{325}}{2 \times 9}
  4. Simplify Expressions: Simplify the expression by calculating the two possible values for gg.\newlineFirst solution: g=1+32518g = \frac{-1 + \sqrt{325}}{18}\newlineSecond solution: g=132518g = \frac{-1 - \sqrt{325}}{18}
  5. Check Decimal Approximations: The square root of 325325 cannot be simplified to an integer or a simple fraction, so we will leave it as 325\sqrt{325}. However, we can check if it simplifies to a decimal rounded to the nearest hundredth.\newlineFirst solution: g(1+18.03)/1817.03/180.95g \approx (-1 + 18.03) / 18 \approx 17.03 / 18 \approx 0.95\newlineSecond solution: g(118.03)/1819.03/181.06g \approx (-1 - 18.03) / 18 \approx -19.03 / 18 \approx -1.06

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