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Solve using the quadratic formula.\newline5u2+8u+2=05u^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.\newline5u2+8u+2=05u^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 5u2+8u+2=05u^2 + 8u + 2 = 0. Compare 5u2+8u+2=05u^2 + 8u + 2 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0. a=5a = 5 b=8b = 8 c=2c = 2
  2. Substitute values: 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}. u=−(8)±(8)2−4⋅5⋅22⋅5u = \frac{-(8) \pm \sqrt{(8)^2 - 4\cdot5\cdot2}}{2\cdot5}
  3. Simplify expression: Simplify the expression under the square root and the denominator. \newlineu=−8±64−4010u = \frac{-8 \pm \sqrt{64 - 40}}{10}\newlineu=−8±2410u = \frac{-8 \pm \sqrt{24}}{10}
  4. Simplify square root: Simplify the square root of 2424.24\sqrt{24} can be simplified to 262\sqrt{6} because 24=4×624 = 4\times6 and 4=2\sqrt{4} = 2.u=−8±2610u = \frac{-8 \pm 2\sqrt{6}}{10}
  5. Split into solutions: Simplify the expression by splitting it into two possible solutions for uu.u=−8+2610u = \frac{{-8 + 2\sqrt{6}}}{{10}} or u=−8−2610u = \frac{{-8 - 2\sqrt{6}}}{{10}}
  6. Simplify fractions: Simplify the fractions to find the solutions for uu.u=−4+65u = \frac{-4 + \sqrt{6}}{5} or u=−4−65u = \frac{-4 - \sqrt{6}}{5}
  7. Round values: If necessary, round the values of uu to the nearest hundredth.\newlineu≈(−4+2.45)/5u \approx (-4 + 2.45) / 5 or u≈(−4−2.45)/5u \approx (-4 - 2.45) / 5\newlineu≈−1.55/5u \approx -1.55 / 5 or u≈−6.45/5u \approx -6.45 / 5\newlineu≈−0.31u \approx -0.31 or u≈−1.29u \approx -1.29

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