SOLUTION: Solve the equation in the real number system. 7x^3+3x^2-29x+11=0 What are the reals solutions of the equation?

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Question 765779: Solve the equation in the real number system. 7x^3+3x^2-29x+11=0
What are the reals solutions of the equation?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
7x%5E3%2B3x%5E2-29x%2B11=0+...factor, write 3x%5E2 as 14x%5E2-11x%5E2 and -29x as -7x-22x
7x%5E3%2B14x%5E2-7x-11x%5E2-22x%2B11=0+......group
%287x%5E3-11x%5E2%29%2B%2814x%5E2-22x%29-%287x-11%29=0+
x%5E2%287x-11%29%2B2x%287x-11%29-%287x-11%29=0+
%287x-11%29%28x%5E2%2B2x-1%29+=+0

solutions:
if 7x-11=+0 => 7x=11=> x=11%2F7
to find other two roots, use quadratic formula and solve x%5E2%2B2x-1+=+0 for x
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+
x+=+%28-2+%2B-+sqrt%28+4%2B4%29%29%2F2+
x+=+%28-2+%2B-+sqrt%28+8%29%29%2F2+
x+=+%28-2+%2B-+2.83%29%2F2+
solutions:
x+=+%28-2+%2B2.83%29%2F2+
x+=+0.83%2F2+
x+=+0.415+
and
x+=+%28-2+-2.83%29%2F2+
x+=-4.83%2F2+
x+=+-2.415+

so, your solutions are: x=11%2F7,x+=+0.415+, and x+=+-2.415+

+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+35%2C7x%5E3%2B3x%5E2-29x%2B11%29+