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Solve using the quadratic formula.\newline4u2+6u6=04u^2 + 6u - 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.\newline4u2+6u6=04u^2 + 6u - 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. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc from the quadratic equation 4u2+6u6=04u^2 + 6u − 6 = 0. Compare 4u2+6u6=04u^2 + 6u − 6 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0. a=4a = 4 bb00 bb11
  2. Substitute values into quadratic formula: Substitute the values of aa, bb, and cc into the quadratic formula u=b±b24ac2au = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substitute a=4a = 4, b=6b = 6, and c=6c = -6 into the formula. u=(6)±(6)244(6)24u = \frac{-(6) \pm \sqrt{(6)^2 - 4\cdot4\cdot(-6)}}{2\cdot4} u=6±36+968u = \frac{-6 \pm \sqrt{36 + 96}}{8}
  3. Simplify expression and calculate discriminant: Simplify the expression under the square root and calculate the discriminant.36+96\sqrt{36 + 96} = 132\sqrt{132}
  4. Continue with quadratic formula: Continue with the quadratic formula using the simplified discriminant.\newlineu=6±1328u = \frac{{-6 \pm \sqrt{132}}}{{8}}\newlineCalculate the two possible solutions for uu.\newlineu=6+1328u = \frac{{-6 + \sqrt{132}}}{{8}} or u=61328u = \frac{{-6 - \sqrt{132}}}{{8}}
  5. Simplify solutions and round: Simplify the solutions and round to the nearest hundredth if necessary.\newlineu=6+1328u = \frac{-6 + \sqrt{132}}{8} or u=61328u = \frac{-6 - \sqrt{132}}{8}\newlineu6+11.498u \approx \frac{-6 + 11.49}{8} or u611.498u \approx \frac{-6 - 11.49}{8}\newlineu5.498u \approx \frac{5.49}{8} or u17.498u \approx \frac{-17.49}{8}\newlineu0.69u \approx 0.69 or u2.19u \approx -2.19

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