Final answer:
To solve the quadratic equation (4k+11)²-100=0, we recognize it as a perfect square, simplify, factor, and find two potential solutions for k: -1/4 and -21/4.
Step-by-step explanation:
The student's question involves solving the quadratic equation (4k+11)²-100=0. To solve this, we can simplify the equation by recognizing that the left side is a perfect square. The equation simplifies to (4k+11-10)(4k+11+10)=0, which further simplifies to (4k+1)(4k+21)=0. Setting each factor equal to zero gives us two possible solutions for k: k=-1/4 and k=-21/4.
The quadratic equation provided in the question differs from the typical form ax² + bx + c = 0, but the process of solving for the variable remains consistent. We simplified the equation by factoring, which is an alternative method to the quadratic formula, useful when the equation is a perfect square or can be easily factored.