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Solve using the quadratic formula.\newlinex2−8x+8=0x^2 - 8x + 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.\newlinex2−8x+8=0x^2 - 8x + 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. Quadratic Formula: The quadratic formula is given by x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. For the equation x2−8x+8=0x^2 - 8x + 8 = 0, a=1a = 1, b=−8b = -8, and c=8c = 8.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. For our equation, the discriminant is (−8)2−4(1)(8)(-8)^2 - 4(1)(8).
  3. Discriminant Calculation: Calculating the discriminant: (−8)2−4(1)(8)=64−32=32(-8)^2 - 4(1)(8) = 64 - 32 = 32.
  4. Apply Quadratic Formula: Now, apply the quadratic formula with the calculated discriminant. x=−(−8)±322×1x = \frac{-(-8) \pm \sqrt{32}}{2 \times 1}.
  5. Simplify Equation: Simplify the equation: x=8±322x = \frac{8 \pm \sqrt{32}}{2}.
  6. Divide by 22: Since 32\sqrt{32} can be simplified to 424\sqrt{2}, the equation becomes x=(8±42)/2x = (8 \pm 4\sqrt{2}) / 2.
  7. Two Solutions: Divide both terms in the numerator by 22: x=4±22x = 4 \pm 2\sqrt{2}.
  8. Approximate 2\sqrt{2}: Now we have two solutions for xx: x=4+22x = 4 + 2\sqrt{2} or x=4−22x = 4 - 2\sqrt{2}. To express these as decimals rounded to the nearest hundredth, we need to calculate the approximate values of 222\sqrt{2}.
  9. Calculate Approximate Values: Approximating 222\sqrt{2}: 22≈2×1.41=2.822\sqrt{2} \approx 2 \times 1.41 = 2.82 (rounded to the nearest hundredth).
  10. Approximate Solutions: Now, calculate the approximate values for xx: x≈4+2.82x \approx 4 + 2.82 or x≈4−2.82x \approx 4 - 2.82.
  11. Approximate Solutions: Now, calculate the approximate values for xx: x≈4+2.82x \approx 4 + 2.82 or x≈4−2.82x \approx 4 - 2.82.The approximate solutions are: x≈6.82x \approx 6.82 or x≈1.18x \approx 1.18, rounded to the nearest hundredth.

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