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# Show all work to solve 3x2 + 5x − 2 = 0.

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Show all work to solve 3x2 + 5x − 2 = 0.

Jan 26, 2023

#1
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$$x = \frac{-5 \pm \sqrt{5^2 - 4(3)(-2)}}{2} = \frac{-5 \pm 7}{2}$$

so the roots are -6 and 1.

Jan 26, 2023
#2
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first, we can do 3x2.

so this would be 6+5x-2=0

Now, we can move all the numbers to the other side by adding or subtracting them on each side

6-6+5x-2+2=0-6+2

or

5x = -4

then divide both sides by 5

x = -4/5

Jan 26, 2023
#3
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I think they meant $$3x^2$$, not 3x.

BuilderBoi  Jan 26, 2023
#4
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To factor the left-hand side, we need 2 numbers that sum to 5 and two numbers that multiply to $$3 \times -2 = -6$$. The only two numbers that work are -1 and 6.

Now, rewrite this equation to $$3x^2 - x + 6x - 2 = 0$$. Just factor $$3x^2 - x$$ to $$x(3x - 1)$$ and factor $$6x - 2$$ to $$2(3x - 1)$$

Adding both of these gives us $$(x+2)(3x-1) = 0$$

If we want the product to be 0, x + 2 = 0, or 3x - 1 = 0.

Can you take it from here?

Jan 26, 2023