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Solve using the quadratic formula.\newline9h2+6h6=09h^2 + 6h - 6 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____

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Q. Solve using the quadratic formula.\newline9h2+6h6=09h^2 + 6h - 6 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineh=h = _____ or h=h = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 9h2+6h6=09h^2 + 6h - 6 = 0.a=9a = 9, b=6b = 6, c=6c = -6
  2. Write quadratic formula: Write down the quadratic formula: h=b±b24ac2ah = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.h=(6)±(6)24(9)(6)2(9)h = \frac{{-(6) \pm \sqrt{{(6)^2 - 4(9)(-6)}}}}{{2(9)}}
  4. Calculate discriminant: Calculate the discriminant (the part under the square root): b24acb^2 - 4ac.\newlineDiscriminant = (6)24(9)(6)=36+216=252(6)^2 - 4(9)(-6) = 36 + 216 = 252
  5. Calculate square root: Calculate the square root of the discriminant. 252=4×63=2×63\sqrt{252} = \sqrt{4 \times 63} = 2 \times \sqrt{63}
  6. Insert back into formula: Insert the square root of the discriminant back into the formula.\newlineh=6±2×632×9h = \frac{-6 \pm 2 \times \sqrt{63}}{2 \times 9}
  7. Simplify expression: Simplify the expression by dividing all terms by the common factor 22.h=3±639h = \frac{{-3 \pm \sqrt{63}}}{{9}}
  8. Calculate possible solutions: Calculate the two possible solutions for hh.h=3+639h = \frac{-3 + \sqrt{63}}{9} or h=3639h = \frac{-3 - \sqrt{63}}{9}
  9. Round values: Round the values of hh to the nearest hundredth, if required.h(3+7.949)h \approx (\frac{-3 + 7.94}{9}) or h(37.949)h \approx (\frac{-3 - 7.94}{9})h4.949h \approx \frac{4.94}{9} or h10.949h \approx \frac{-10.94}{9}h0.55h \approx 0.55 or h1.21h \approx -1.21

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