Math  /  Algebra

QuestionSolve the equation using the quadratic formula: 4n2=12n74 n^{2} = -12 n - 7. Provide exact and approximate solutions.

Studdy Solution
To find the approximate solutions, calculate the values of .5+0.52-.5 +0.5\sqrt{2} and .50.52-.5 -0.5\sqrt{2}.
n.5+0.520.646n \approx -.5 +0.5\sqrt{2} \approx -0.646n.50.522.354n \approx -.5 -0.5\sqrt{2} \approx -2.354So, the solutions to the equation 4n2+12n+7=04n^{2} +12n +7 =0 are n=.5±0.52n = -.5 \pm0.5\sqrt{2} (exact) and n0.646,2.354n \approx -0.646, -2.354 (approximate).

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