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Solve using the quadratic formula.\newline4w2−4w−4=04w^2 - 4w - 4 = 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.\newline4w2−4w−4=04w^2 - 4w - 4 = 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 4w2−4w−4=04w^2 - 4w - 4 = 0, the coefficients are:\newlinea = 44\newlineb = −4-4\newlinec = −4-4
  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 we get:\newlinew=−(−4)±(−4)2−4⋅4⋅(−4)2⋅4w = \frac{-(-4) \pm \sqrt{(-4)^2 - 4\cdot4\cdot(-4)}}{2\cdot4}
  3. Simplify under square root: Simplify the equation under the square root.\newlineCalculate the discriminant b2−4acb^2 - 4ac:\newlineDiscriminant = (−4)2−4⋅4⋅(−4)(-4)^2 - 4\cdot4\cdot(-4)\newlineDiscriminant = 16+6416 + 64\newlineDiscriminant = 8080
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the discriminant. w=4±808w = \frac{4 \pm \sqrt{80}}{8}
  5. Simplify square root: Simplify the square root of the discriminant. 80\sqrt{80} can be simplified to 16×5\sqrt{16\times 5}, which is 4×54\times\sqrt{5}. w=4±4×58w = \frac{4 \pm 4\times\sqrt{5}}{8}
  6. Divide by common factor: Simplify the equation by dividing by the common factor.\newlineBoth terms in the numerator have a common factor of 44, so we can simplify:\newlinew=1±52w = \frac{1 \pm \sqrt{5}}{2}
  7. Calculate possible solutions: Calculate the two possible solutions for ww.w=1+52w = \frac{1 + \sqrt{5}}{2} or w=1−52w = \frac{1 - \sqrt{5}}{2}
  8. Round values: Round the values of ww to the nearest hundredth, if required.w≈(1+2.24)/2w \approx (1 + 2.24) / 2 or w≈(1−2.24)/2w \approx (1 - 2.24) / 2w≈3.24/2w \approx 3.24 / 2 or w≈−1.24/2w \approx -1.24 / 2w≈1.62w \approx 1.62 or w≈−0.62w \approx -0.62

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