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Solve using the quadratic formula.\newline5u2+7u6=05u^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.\newline5u2+7u6=05u^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. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 5u2+7u6=05u^2 + 7u - 6 = 0.a=5a = 5, b=7b = 7, c=6c = -6
  2. Write quadratic formula: Write down the quadratic formula: u=b±b24ac2au = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.u=(7)±(7)245(6)25u = \frac{{-(7) \pm \sqrt{{(7)^2 - 4\cdot5\cdot(-6)}}}}{{2\cdot5}}
  4. Simplify discriminant: Simplify the expression under the square root (the discriminant). (7)245(6)=49+120=169\sqrt{(7)^2 - 4\cdot 5\cdot (-6)} = \sqrt{49 + 120} = \sqrt{169}
  5. Calculate square root: Calculate the square root of the discriminant. 169=13\sqrt{169} = 13
  6. Substitute back: Substitute the square root back into the quadratic formula. u=7±132×5u = \frac{{-7 \pm 13}}{{2 \times 5}}
  7. Calculate solutions: Calculate the two possible solutions for uu.u=7+1310u = \frac{{-7 + 13}}{{10}} or u=71310u = \frac{{-7 - 13}}{{10}}u=610u = \frac{6}{10} or u=2010u = \frac{-20}{10}
  8. Simplify fractions: Simplify the fractions to their simplest form. u=35u = \frac{3}{5} or u=2u = -2
  9. Round solutions: If necessary, round the solutions to the nearest hundredth. u=0.60u = 0.60 or u=2.00u = -2.00

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