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Solve using the quadratic formula.\newline2s2+7s−2=02s^2 + 7s - 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____

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Q. Solve using the quadratic formula.\newline2s2+7s−2=02s^2 + 7s - 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 2s2+7s−2=02s^2 + 7s - 2 = 0.\newlinea=2a = 2, b=7b = 7, c=−2c = -2
  2. Write quadratic formula: Write down the quadratic formula: s=−b±b2−4ac2as = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.\newlines=−(7)±(7)2−4⋅2⋅(−2)2⋅2s = \frac{-(7) \pm \sqrt{(7)^2 - 4\cdot2\cdot(-2)}}{2\cdot2}
  4. Simplify discriminant: Simplify the expression under the square root (the discriminant). (7)2−4⋅2⋅(−2)=49+16=65\sqrt{(7)^2 - 4\cdot 2\cdot (-2)} = \sqrt{49 + 16} = \sqrt{65}
  5. Insert discriminant: Insert the value of the discriminant back into the quadratic formula.\newlines=−7±654s = \frac{-7 \pm \sqrt{65}}{4}
  6. Calculate solutions: Calculate the two possible solutions for ss.s=−7+654s = \frac{{-7 + \sqrt{65}}}{{4}} or s=−7−654s = \frac{{-7 - \sqrt{65}}}{{4}}
  7. Round values: Round the values of ss to the nearest hundredth, if necessary.s≈(−7+8.06)/4s \approx (-7 + 8.06) / 4 or s≈(−7−8.06)/4s \approx (-7 - 8.06) / 4s≈1.06/4s \approx 1.06 / 4 or s≈−15.06/4s \approx -15.06 / 4s≈0.27s \approx 0.27 or s≈−3.77s \approx -3.77

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