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Solve using the quadratic formula.\newlinek2+4k+4=0k^2 + 4k + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____

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Q. Solve using the quadratic formula.\newlinek2+4k+4=0k^2 + 4k + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____
  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 k2+4k+4=0k^2 + 4k + 4 = 0, the coefficients are:\newlinea = 11, b = 44, and c = 44.
  2. Write formula: Write down the quadratic formula.\newlineThe quadratic formula is given by k=−b±b2−4ac2ak = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute coefficients: Substitute the coefficients into the quadratic formula.\newlineSubstitute a=1a = 1, b=4b = 4, and c=4c = 4 into the formula to get:\newlinek=(−(4)±(4)2−4(1)(4))/(2(1))k = (-(4) \pm \sqrt{(4)^2 - 4(1)(4)}) / (2(1)).
  4. Simplify square root: Simplify under the square root.\newlineCalculate the discriminant b2−4acb^2 - 4ac:\newline(4)2−4(1)(4)=16−16=0(4)^2 - 4(1)(4) = 16 - 16 = 0.
  5. Simplify formula: Simplify the quadratic formula with the discriminant.\newlineSince the discriminant is 00, the square root of 00 is 00, so the formula simplifies to:\newlinek=(−(4)±0)/(2(1))k = (-(4) \pm 0) / (2(1)).
  6. Solve for kk: Solve for kk.\newlineSimplify the expression to find the value of kk:\newlinek=(−4)/2=−2k = (-4) / 2 = -2.\newlineSince the discriminant is 00, there is only one real solution.

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