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Solve using the quadratic formula.\newline7w2+3w−7=07w^2 + 3w - 7 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____

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Q. Solve using the quadratic formula.\newline7w2+3w−7=07w^2 + 3w - 7 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 7w2+3w−7=07w^2 + 3w - 7 = 0.a=7a = 7, b=3b = 3, c=−7c = -7
  2. Write quadratic formula: Write down the quadratic formula: w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.w=−(3)±(3)2−4(7)(−7)2(7)w = \frac{{-(3) \pm \sqrt{{(3)^2 - 4(7)(-7)}}}}{{2(7)}}
  4. Simplify discriminant: Simplify the expression under the square root (the discriminant). (3)2−4(7)(−7)=9+196=205\sqrt{(3)^2 - 4(7)(-7)} = \sqrt{9 + 196} = \sqrt{205}
  5. Insert discriminant: Insert the value of the discriminant back into the quadratic formula. w=−3±20514w = \frac{-3 \pm \sqrt{205}}{14}
  6. Calculate solutions: Calculate the two possible solutions for ww.w=−3+20514w = \frac{{-3 + \sqrt{205}}}{{14}} or w=−3−20514w = \frac{{-3 - \sqrt{205}}}{{14}}
  7. Round values: Round the values of ww to the nearest hundredth, if necessary.w \approx (\-3 + 14.32) / 14 or w \approx (\-3 - 14.32) / 14w≈11.32/14w \approx 11.32 / 14 or w≈−17.32/14w \approx -17.32 / 14w≈0.81w \approx 0.81 or w≈−1.24w \approx -1.24

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