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Solve using the quadratic formula.\newlineu2−7u+6=0u^2 - 7u + 6 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____

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Q. Solve using the quadratic formula.\newlineu2−7u+6=0u^2 - 7u + 6 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____
  1. Quadratic Formula: The quadratic formula is given by u=−b±b2−4ac2au = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation au2+bu+c=0au^2 + bu + c = 0. In this case, a=1a = 1, b=−7b = -7, and c=6c = 6.
  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 (−7)2−4(1)(6)(-7)^2 - 4(1)(6).
  3. Perform Calculation: Perform the calculation: (−7)2−4(1)(6)=49−24=25(-7)^2 - 4(1)(6) = 49 - 24 = 25.
  4. Apply Quadratic Formula: Now, apply the quadratic formula with the calculated discriminant. Since the discriminant is a perfect square, we will get exact values for uu.u=−(−7)±252×1u = \frac{-(-7) \pm \sqrt{25}}{2 \times 1}
  5. Simplify Equation: Simplify the equation: u=7±52u = \frac{7 \pm 5}{2}.
  6. Find Possible Values: Find the two possible values for uu by doing the addition and subtraction separately:\newlineu=(7+5)/2u = (7 + 5) / 2 and u=(7−5)/2u = (7 - 5) / 2.
  7. Calculate Values: Calculate the two values: u=122u = \frac{12}{2} and u=22u = \frac{2}{2}.
  8. Final Answers: Simplify the fractions to get the final answers: u=6u = 6 and u=1u = 1.

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