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Solve using the quadratic formula.\newline6x2−2x−4=06x^2 - 2x - 4 = 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.\newline6x2−2x−4=06x^2 - 2x - 4 = 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. Identify coefficients: Identify the coefficients of the quadratic equation 6x2−2x−4=06x^2 - 2x - 4 = 0. The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0. Here, a=6a = 6, b=−2b = -2, and c=−4c = -4.
  2. Recall quadratic formula: Recall the quadratic formula, which is x=−b±b2−4ac2ax = \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=−(−2)±(−2)2−4⋅6⋅(−4)2⋅6x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4\cdot6\cdot(-4)}}{2\cdot6}.
  4. Simplify equation: Simplify the equation by calculating the values inside the square root and the constants outside. This gives us x=2±4+9612x = \frac{2 \pm \sqrt{4 + 96}}{12}.
  5. Further simplify square root: Further simplify the square root. 4+96=100=10\sqrt{4 + 96} = \sqrt{100} = 10. Now we have x=2±1012x = \frac{2 \pm 10}{12}.
  6. Solve for x values: Solve for the two possible values of x. The first solution is x=(2+10)/12=12/12=1x = (2 + 10) / 12 = 12 / 12 = 1. The second solution is x=(2−10)/12=−8/12=−2/3x = (2 - 10) / 12 = -8 / 12 = -2/3 after simplifying the fraction.

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