SOLUTION: find the real solutions of 7x^3+3x^2-29x+11

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Question 1085735: find the real solutions of 7x^3+3x^2-29x+11
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+7x%5E3%2B3x%5E2-29x%2B11=0

+7x%5E3%2B14x%5E2-11x%5E2-7x-22x%2B11=0...factor
+%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+%2B+2x+-+1%29+=+0
solutions:
if +%287x+-+11%29+=+0->7x=11->x=11%2F7
if
+x%5E2+%2B+2x+-+1+=+0....use quadratic formula
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+2%2A4+%29%29%2F2+
x+=+%28-2+%2B-+2sqrt%28+2+%29%29%2F2+
x+=+%28-cross%282%291+%2B-+cross%282%29sqrt%28+2+%29%29%2Fcross%282%291+
x+=+%28-1+%2B-+sqrt%28+2+%29%29+
solutions:
x+=+-1+%2B+sqrt%28+2+%29+ approximately x+=+0.41+
or
x+=+-1+-+sqrt%28+2+%29+ approximately x+=-2.41+

so, your solutions are:
x=11%2F7->approximately x+=+1.57+
x+=+-1+%2B+sqrt%28+2+%29+-> approximately x+=+0.41+
x+=+-1+-+sqrt%28+2+%29+ -> approximately x+=-2.41+