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Solve using the quadratic formula.\newline7u2+8u+2=07u^2 + 8u + 2 = 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.\newline7u2+8u+2=07u^2 + 8u + 2 = 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. Identify values: Identify the values of aa, bb, and cc in the quadratic equation 7u2+8u+2=07u^2 + 8u + 2 = 0. The quadratic equation is in the form au2+bu+c=0au^2 + bu + c = 0, so by comparison: a=7a = 7 b=8b = 8 c=2c = 2
  2. Substitute in formula: Substitute the values of aa, bb, and cc into the quadratic formula to find uu. The quadratic formula is u=−b±b2−4ac2au = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get: u=−(8)±(8)2−4⋅7⋅22⋅7u = \frac{-(8) \pm \sqrt{(8)^2 - 4\cdot7\cdot2}}{2\cdot7}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (8)2−4⋅7⋅2=64−56=8\sqrt{(8)^2 - 4\cdot7\cdot2} = \sqrt{64 - 56} = \sqrt{8}
  4. Continue simplifying: Continue simplifying the quadratic formula with the values we have.\newlineu=−8±814u = \frac{-8 \pm \sqrt{8}}{14}\newlineSince 8\sqrt{8} can be simplified to 222\sqrt{2}, we can rewrite the equation as:\newlineu=−8±2214u = \frac{-8 \pm 2\sqrt{2}}{14}
  5. Divide by 22: Simplify the expression by dividing all terms by 22.\newlineu=−4±27u = \frac{-4 \pm \sqrt{2}}{7}
  6. Identify possible values: Identify the two possible values for uu.u=−4+27u = \frac{-4 + \sqrt{2}}{7} or u=−4−27u = \frac{-4 - \sqrt{2}}{7}
  7. Round to nearest hundredth: Round the values of uu to the nearest hundredth, if necessary.u≈(−4+1.41)/7u \approx (-4 + 1.41) / 7 or u≈(−4−1.41)/7u \approx (-4 - 1.41) / 7u≈−2.59/7u \approx -2.59 / 7 or u≈−5.41/7u \approx -5.41 / 7u≈−0.37u \approx -0.37 or u≈−0.77u \approx -0.77

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