SOLUTION: I am stumped, I just do not know the steps, I would greatly appreciate any help on this. Thank you! Solve using the quadratic formula. Then use a calculator to approximate, to

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: I am stumped, I just do not know the steps, I would greatly appreciate any help on this. Thank you! Solve using the quadratic formula. Then use a calculator to approximate, to       Log On


   

Question 613730: I am stumped, I just do not know the steps, I would greatly appreciate any help on this. Thank you!
Solve using the quadratic formula. Then use a calculator to approximate, to three decimal places, the solutions as rational numbers.
46.
x^2 + 6x + 4 = 0


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B6x%2B4=0 Start with the given equation.


Notice that the quadratic x%5E2%2B6x%2B4 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=4


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%284%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=4


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%284%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-16+%29%29%2F%282%281%29%29 Multiply 4%281%29%284%29 to get 16


x+=+%28-6+%2B-+sqrt%28+20+%29%29%2F%282%281%29%29 Subtract 16 from 36 to get 20


x+=+%28-6+%2B-+sqrt%28+20+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+2%2Asqrt%285%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-6%29%2F%282%29+%2B-+%282%2Asqrt%285%29%29%2F%282%29 Break up the fraction.


x+=+-3+%2B-+sqrt%285%29 Reduce.


x+=+-3%2Bsqrt%285%29 or x+=+-3-sqrt%285%29 Break up the expression.


So the exact solutions are x+=+-3%2Bsqrt%285%29 or x+=+-3-sqrt%285%29


Then use a calculator to find the approximate solutions to be x=-0.7639320225 or x=-5.236067978


Then round those approximate solutions to three places to get x=-0.764 or x=-5.236
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