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Andreas93 [3]
3 years ago
11

Need help to do this step by step please 3x2 - 2x=-1

Mathematics
1 answer:
sdas [7]3 years ago
8 0

Answer:

Solving the expression 3x^2-2x=-1 we get: \mathbf{x=\frac{1+\sqrt{2}i }{3}\:or\:x=\frac{1-\sqrt{2}i }{3}}

Step-by-step explanation:

We need to solve the expression: 3x^2-2x=-1

This is a quadratic expression and it can be solved using quadratic formula

Solving:

3x^2-2x=-1\\

we can write it as:

3x^2-2x+1=0

The quadratic formula is: x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

where a = 3, b = -2 and c= 1

Putting values and solving:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(3)(1)}}{2(3)}\\x=\frac{2\pm\sqrt{4-12}}{2(3)}\\x=\frac{2\pm\sqrt{-8}}{6}\\We\:know\:that\:\sqrt{-1}=i\\x=\frac{2\pm\sqrt{8}\sqrt{-1} }{6} \\We\:know\:\sqrt{8}=\sqrt{2\times 2 \times 2}=\sqrt{2^2 \times 2}=2\sqrt{2}   \\x=\frac{2\pm2\sqrt{2}i }{6}\\Now,\\x=\frac{2+2\sqrt{2}i }{6}\:or\:x=\frac{2-2\sqrt{2}i }{6}\\x=\frac{2(1+\sqrt{2}i) }{6}\:or\:x=\frac{2(1-\sqrt{2}i) }{6}\\x=\frac{1+\sqrt{2}i }{3}\:or\:x=\frac{1-\sqrt{2}i }{3}

So, solving the expression 3x^2-2x=-1 we get: \mathbf{x=\frac{1+\sqrt{2}i }{3}\:or\:x=\frac{1-\sqrt{2}i }{3}}

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