SOLUTION: Using the quadratic formula to solve for the roots. Given {{{3x^2+3x-2=0}}} I think it's ax2+bx+c=0 but I get lost on how to work it out.

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Question 1176837: Using the quadratic formula to solve for the roots.
Given 3x%5E2%2B3x-2=0
I think it's ax2+bx+c=0 but I get lost on how to work it out.
Found 3 solutions by math_tutor2020, josgarithmetic, Solver92311:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The ax^2+bx+c = 0 is known as standard form for a quadratic. Compare that to what you were given and we see that
a = 3
b = 3
c = -2

Those values are then plugged into the quadratic formula below. I broke up the "plus/minus" to form two separate equations.
x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 or x+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-3%2Bsqrt%28%283%29%5E2-4%283%29%28-2%29%29%29%2F%282%283%29%29 or x+=+%28-3-sqrt%28%283%29%5E2-4%283%29%28-2%29%29%29%2F%282%283%29%29

x+=+%28-3%2Bsqrt%2833%29%29%2F%286%29 or x+=+%28-3-sqrt%2833%29%29%2F%286%29 Exact Solutions

x+=+%28-3%2B5.74456264653803%29%2F%286%29 or x+=+%28-3-5.74456264653803%29%2F%286%29 Use a calculator from here.

x+=+%282.74456264653803%29%2F%286%29 or x+=+%28-8.74456264653803%29%2F%286%29

x+=+0.457427107756338 or x+=+-1.45742710775634 Values are approximate

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So to recap, the exact solutions are:
x+=+%28-3%2Bsqrt%2833%29%29%2F%286%29 or x+=+%28-3-sqrt%2833%29%29%2F%286%29
which approximate to
x+=+0.457427107756338 or x+=+-1.45742710775634
in that exact order given

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
ax%5E2%2Bbx%2Bc=0
ax%5E2%2Bbx=-c
a%28x%5E2%2Bbx%2Fa%29=-c
x%5E2%2Bbx%2Fa=-c%2Fa
x%5E2%2Bbx%2Fa%2B%28b%2F%282a%29%29%5E2=b%2F%282a%29%5E2-c%2Fa
%28x%2Bb%2F%282a%29%29%5E2=b%2F%284a%5E2%29-c%2Fa
%28x%2Bb%2F%282a%29%29%5E2=b%2F%284a%5E2%29-%28c%2Fa%29%28%284a%29%2F%284a%29%29
%28x%2Bb%2F%282a%29%29%5E2=%28b-4ac%29%2F%284a%5E2%29
x%2Bb%2F%282a%29=sqrt%28b-4ac%29%2F%282a%29
x=-b%2F%282a%29%2B-+sqrt%28b-4ac%29%2F%282a%29
highlight_green%28x=%28-b%2B-+sqrt%28b-4ac%29%29%2F%282a%29%29---------Use this formula to solve your example.

Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


Quadratic Formula

The two roots of are:



The character of the roots:

: Two distinct real number roots.

: One root with a multiplicity of two.

: A conjugate pair of complex number roots.

Plug your given coefficients into the formula and do the arithmetic. Your roots will be real and irrational, so I would leave them in radical form.

John

My calculator said it, I believe it, that settles it

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