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Solve using the quadratic formula.\newline4u2+6u+1=04u^2 + 6u + 1 = 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.\newline4u2+6u+1=04u^2 + 6u + 1 = 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 4u2+6u+1=04u^2 + 6u + 1 = 0. The quadratic equation is in the form au2+bu+c=0au^2 + bu + c = 0, so by comparison: a=4a = 4 b=6b = 6 c=1c = 1
  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=−(6)±(6)2−4⋅4⋅12⋅4u = \frac{-(6) \pm \sqrt{(6)^2 - 4\cdot4\cdot1}}{2\cdot4}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (6)2−4⋅4⋅1=36−16=20\sqrt{(6)^2 - 4\cdot 4\cdot 1} = \sqrt{36 - 16} = \sqrt{20}
  4. Continue simplifying: Continue simplifying the quadratic formula with the values we have.\newlineu=−6±208u = \frac{-6 \pm \sqrt{20}}{8}\newlineSince 20\sqrt{20} can be simplified to 252\sqrt{5}, we can rewrite the equation as:\newlineu=−6±258u = \frac{-6 \pm 2\sqrt{5}}{8}
  5. Divide by 22: Simplify the expression by dividing both terms in the numerator by 22.\newlineu=−3±54u = \frac{-3 \pm \sqrt{5}}{4}
  6. Identify possible values: Identify the two possible values for uu.u=−3+54u = \frac{{-3 + \sqrt{5}}}{{4}} or u=−3−54u = \frac{{-3 - \sqrt{5}}}{{4}}
  7. Round to nearest hundredth: Round the values of uu to the nearest hundredth, if necessary.u≈(−3+2.244)u \approx (\frac{-3 + 2.24}{4}) or u≈(−3−2.244)u \approx (\frac{-3 - 2.24}{4})u≈−0.764u \approx \frac{-0.76}{4} or u≈−5.244u \approx \frac{-5.24}{4}u≈−0.19u \approx -0.19 or u≈−1.31u \approx -1.31

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