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Solve using the quadratic formula.\newline2x2−9x−1=02x^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.\newline2x2−9x−1=02x^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 Quadratic Formula: The quadratic formula is given by x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=2a = 2, b=−9b = -9, and c=−1c = -1.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is (−9)2−4(2)(−1)=81+8=89(-9)^2 - 4(2)(-1) = 81 + 8 = 89.
  3. Apply Quadratic Formula: Now, apply the quadratic formula using the values of aa, bb, and cc:x=−(−9)±892×2x = \frac{-(-9) \pm \sqrt{89}}{2 \times 2}x=9±894x = \frac{9 \pm \sqrt{89}}{4}
  4. Find Two Solutions: Since 89\sqrt{89} cannot be simplified further, we will have two solutions for xx, one with the plus sign and one with the minus sign:\newlinex=(9+89)/4x = (9 + \sqrt{89}) / 4 or x=(9−89)/4x = (9 - \sqrt{89}) / 4
  5. Express Solutions as Decimals: To express the solutions as decimals rounded to the nearest hundredth, we calculate each one:\newlinex≈(9+89)/4≈(9+9.43)/4≈18.43/4≈4.61x \approx (9 + \sqrt{89}) / 4 \approx (9 + 9.43) / 4 \approx 18.43 / 4 \approx 4.61\newlinex≈(9−89)/4≈(9−9.43)/4≈−0.43/4≈−0.11x \approx (9 - \sqrt{89}) / 4 \approx (9 - 9.43) / 4 \approx -0.43 / 4 \approx -0.11

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