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Question 815623: Solve the following quadratic both by completing the square and quadratic formula. Leave your answer in simplest radical form.
3x^2-4x-1=1
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! 3x^2 - 4x - 1 = 1
3x^2 - 4x - 2 = 0
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3x^2 - 4x - 2 = 0
x^2 - (4/3)x - (2/3) = 0
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a=1 b=(-4/3) c=(-2/3)
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completing the square:
add (b/2)^2
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x^2 - (4/3)x + ((-4/3)(1/2))^2 = (2/3) + ((-4/3)(1/2))^2
x^2 - (4/3)x + (-2/3)^2 = (2/3) + (-2/3)^2
x^2 - (4/3)x + (-2/3)^2 = (6/9) + (4/9)
(x - 2/3)^2 = (10/9)
x - 2/3 = sqrt(10/9)
x = sqrt(10/9) + 2/3
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x = sqrt(10/9) + 2/3
or
x = 1.72076
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quadratic formula:
the above quadratic equation is in standard form, with a=1 b=(-4/3) c=(-2/3)
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to solve the quadratic equation, plug this:
1 -1.333333 -0.666666
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the roots of the quadratic are:
1.72076
-0.387426
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note that by the quadratic formula we obtain two distinct roots, both of which are valid solutions to the quadratic equation, whereas by completing the square we only obtain one valid solution.
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