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Solve using the quadratic formula.\newlinew2−6w+1=0w^2 - 6w + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____

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Q. Solve using the quadratic formula.\newlinew2−6w+1=0w^2 - 6w + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____
  1. Identify coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form ax2+bx+c=0ax^2 + bx + c = 0. For the equation w2−6w+1=0w^2 - 6w + 1 = 0, the coefficients are:\newlinea=1a = 1, b=−6b = -6, and c=1c = 1.
  2. Write formula: Write down the quadratic formula.\newlineThe quadratic formula is w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute coefficients: Substitute the coefficients into the quadratic formula.\newlinew=−(−6)±(−6)2−4(1)(1)2(1)w = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(1)}}{2(1)}\newlinew=6±36−42w = \frac{6 \pm \sqrt{36 - 4}}{2}\newlinew=6±322w = \frac{6 \pm \sqrt{32}}{2}
  4. Simplify square root: Simplify the expression under the square root.\newline32\sqrt{32} can be simplified to (16×2)\sqrt{(16 \times 2)}, which is 424\sqrt{2}.\newlinew=(6±42)2w = \frac{(6 \pm 4\sqrt{2})}{2}
  5. Divide terms: Simplify the equation by dividing the terms by 22.w=3±222w = \frac{3 \pm 2\sqrt{2}}{2}
  6. Write solutions: Write the solutions as two separate values.\newlinew=3+22w = 3 + 2\sqrt{2} or w=3−22w = 3 - 2\sqrt{2}
  7. Approximate solutions: If necessary, approximate the solutions to the nearest hundredth.\newlinew≈3+2(1.41)w \approx 3 + 2(1.41) or w≈3−2(1.41)w \approx 3 - 2(1.41)\newlinew≈3+2.82w \approx 3 + 2.82 or w≈3−2.82w \approx 3 - 2.82\newlinew≈5.82w \approx 5.82 or w≈0.18w \approx 0.18

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