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Solve using the quadratic formula.\newlinew2−8w−6=0w^2 - 8w - 6 = 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.\newlinew2−8w−6=0w^2 - 8w - 6 = 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 given by w2−8w−6=0w^2 - 8w - 6 = 0. We can compare this with the standard form ax2+bx+c=0ax^2 + bx + c = 0 to find the coefficients.\newlineHere, a=1a = 1, b=−8b = -8, and c=−6c = -6.
  2. Substitute into formula: Substitute the coefficients into the quadratic formula.\newlineThe quadratic formula is w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values of aa, bb, and cc, we get:\newlinew=−(−8)±(−8)2−4⋅1⋅(−6)2⋅1w = \frac{-(-8) \pm \sqrt{(-8)^2 - 4\cdot1\cdot(-6)}}{2\cdot1}\newlinew=8±64+242w = \frac{8 \pm \sqrt{64 + 24}}{2}
  3. Simplify and solve: Simplify under the square root and solve for ww. First, we calculate the value under the square root: 64+24=88\sqrt{64 + 24} = \sqrt{88} Now, we have: w=8±882w = \frac{8 \pm \sqrt{88}}{2}
  4. Simplify square root: Simplify the square root, if possible.\newlineThe square root of 8888 can be simplified to 4×22\sqrt{4\times22} which is 2×222\times\sqrt{22}. So we have:\newlinew=8±2×222w = \frac{8 \pm 2\times\sqrt{22}}{2}
  5. Divide by 22: Simplify the expression by dividing by 22.\newlineWe can divide both terms in the numerator by 22 to simplify the expression:\newlinew=4±222w = \frac{4 \pm \sqrt{22}}{2}
  6. Write final solutions: Write the final solutions.\newlineThe two possible solutions for ww are:\newlinew=4+22w = 4 + \sqrt{22} or w=4−22w = 4 - \sqrt{22}\newlineTo round to the nearest hundredth, we calculate the decimal values:\newlinew≈4+4.69w \approx 4 + 4.69 or w≈4−4.69w \approx 4 - 4.69\newlinew≈8.69w \approx 8.69 or w≈−0.69w \approx -0.69

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