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Solve using the quadratic formula.\newlinex2+x−8=0x^2 + x - 8 = 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.\newlinex2+x−8=0x^2 + x - 8 = 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 x2+x−8=0x^2 + x - 8 = 0. The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0. Here, a=1a = 1, b=1b = 1, and c=−8c = -8.
  2. Recall quadratic formula: Recall the quadratic formula: 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 into formula: Substitute the coefficients aa, bb, and cc into the quadratic formula.x=−(1)±(1)2−4(1)(−8)2(1)x = \frac{{-\left(1\right) \pm \sqrt{{\left(1\right)^2 - 4\left(1\right)\left(-8\right)}}}}{{2\left(1\right)}}x=−1±1+322x = \frac{{-1 \pm \sqrt{1 + 32}}}{{2}}x=−1±332x = \frac{{-1 \pm \sqrt{33}}}{{2}}
  4. Calculate discriminant: Calculate the discriminant 33\sqrt{33} and simplify the expression.\newline33\sqrt{33} is an irrational number, so we will leave it under the square root.\newlinex=−1+332x = \frac{-1 + \sqrt{33}}{2} or x=−1−332x = \frac{-1 - \sqrt{33}}{2}
  5. Write final solutions: Write the final solutions.\newlineThe solutions are x=−1+332x = \frac{-1 + \sqrt{33}}{2} or x=−1−332x = \frac{-1 - \sqrt{33}}{2}.\newlineThese cannot be simplified to integers or fractions, so we will leave them in this form.

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