Question 758250: can you show me step by step on how Solve the quadratic equation by completing the square -3x^2+7x=-5 Found 2 solutions by josgarithmetic, lwsshak3:Answer by josgarithmetic(39616) (Show Source):
Factor a on the left-hand member; this will make the expression there easier to understand and use.
Thinking about the quadratic expression , you can think of it like a rectangle, build with side lengths and . You could draw this and label the two different sides. The area for this rectangle is the expression, . If you assume the longer side is the binomial ( seems intuitively wrong, but do not worry about that), you can cut it in half and remove the piece and place it along the other direction side of the rectangle ---- forming a square which has a corner square piece missing. THAT is the square which we will ADD to both sides of the equation in order to COMPLETE THE SQUARE. You will find when you analyze the drawing so far made, that is this square piece.
Compute the value of this square piece: .
Now, add this term to both sides:
Note very carefully how accounting for the presence of the -3 factor on the left side and the adjustment for this was made on the righthand side.
SIMPLIFY and put into standard form. As you do this simplifcation, be aware you have created a square trinomial on the left hand side. YOU FACTOR that square trinomial:
You can put this solution on YOUR website! Solve the quadratic equation by completing the square
-3x^2+7x=-5
-3x^2+7x+5=0
3x^2-7x-5=0
complete the square
3(x^2-7/3x+49/36)-49/12-5=0
3(x-7/6)^2-49/12-60/12=0
3(x-7/6)^2-109/12=0
x-7/6)^2=109/36
take sqrt of both sides
x-7/6=±√109/6
x=1.17±1.74
x=2.906
or
x=- 0.57
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