Solve using the quadratic formula.9g2+g−9=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.g=_____ or g=_____
Q. Solve using the quadratic formula.9g2+g−9=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.g=_____ or g=_____
Quadratic Formula Explanation: The quadratic formula is given by g=2a−b±b2−4ac, where a, b, and c are the coefficients from the quadratic equation in the form of ax2+bx+c=0. For the equation 9g2+g−9=0, a=9, b=1, and c=−9.
Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4ac. For our equation, the discriminant is 12−4(9)(−9)=1+324=325.
Plug Values into Formula: Now, plug the values of a, b, and the discriminant into the quadratic formula to find the two possible values for g.g=2×9−1±325
Simplify Expressions: Simplify the expression by calculating the two possible values for g.First solution: g=18−1+325Second solution: g=18−1−325
Check Decimal Approximations: The square root of 325 cannot be simplified to an integer or a simple fraction, so we will leave it as 325. However, we can check if it simplifies to a decimal rounded to the nearest hundredth.First solution: g≈(−1+18.03)/18≈17.03/18≈0.95Second solution: g≈(−1−18.03)/18≈−19.03/18≈−1.06
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