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Solve using the quadratic formula.\newline9x2+7x7=09x^2 + 7x - 7 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____

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Q. Solve using the quadratic formula.\newline9x2+7x7=09x^2 + 7x - 7 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____
  1. \newline \newline
  2. Recall quadratic formula: Recall the quadratic formula, which is x=b±b24ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. We will use this formula to find the values of xx.
  3. Substitute coefficients: Substitute the coefficients aa, bb, and cc into the quadratic formula. This gives us x=(7)±(7)24(9)(7)2(9)x = \frac{-(7) \pm \sqrt{(7)^2 - 4(9)(-7)}}{2(9)}.
  4. Calculate discriminant: Calculate the discriminant, which is the part under the square root in the quadratic formula: b24acb^2 - 4ac. This is (7)24(9)(7)=49+252=301(7)^2 - 4(9)(-7) = 49 + 252 = 301.
  5. Insert discriminant: Insert the discriminant back into the quadratic formula: x=7±30118x = \frac{{-7 \pm \sqrt{301}}}{{18}}.
  6. Simplify square root: Simplify the square root of the discriminant if possible. Since 301301 is not a perfect square, we leave it as 301\sqrt{301}.
  7. Calculate positive solution: Calculate the two possible values for x using the plus and minus in the quadratic formula. First, the positive solution: x=7+30118x = \frac{-7 + \sqrt{301}}{18}.
  8. Calculate negative solution: Calculate the negative solution: x=730118x = \frac{{-7 - \sqrt{301}}}{{18}}.
  9. Express solutions as decimals: Since the square root of 301301 cannot be simplified further, we can express the solutions as decimals if required. The decimal approximations are x(7+301)/180.79x \approx (-7 + \sqrt{301}) / 18 \approx 0.79 and x(7301)/181.46x \approx (-7 - \sqrt{301}) / 18 \approx -1.46, rounded to the nearest hundredth.

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