What are the solutions to the equation X^2=3(X-1) ?

The solutions to the equation X^2=3(X-1) are X= 3/2+i(sqrt(3))/2 ,X= 3/2-i(sqrt(3))/2

Find the zeros of X^2=3(X-1)

The zeros of X^2=3(X-1) are X= 3/2+i(sqrt(3))/2 ,X= 3/2-i(sqrt(3))/2

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X^{2} = 3 (X - 1)

X = \frac{3}{2} + i \frac{3}{2}, X = \frac{3}{2} - i \frac{3}{2}

Solution steps

X^{2} = 3 (X - 1)

Expand

3 (X - 1) : 3 X - 3

X^{2} = 3 X - 3

Move

3

to the left side

X^{2} + 3 = 3 X

Move

3 X

to the left side

X^{2} + 3 - 3 X = 0

Write in the standard form

a x^{2} + b x + c = 0

X^{2} - 3 X + 3 = 0

Solve with the quadratic formula

X_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot 3}{2 \cdot 1}

Simplify

(- 3)^{2} - 4 \cdot 1 \cdot 3 : 3 i

X_{1, 2} = \frac{- ( - 3 ) \pm 3 i}{2 \cdot 1}

Separate the solutions

X_{1} = \frac{- ( - 3 ) + 3 i}{2 \cdot 1}, X_{2} = \frac{- ( - 3 ) - 3 i}{2 \cdot 1}

X = \frac{- ( - 3 ) + 3 i}{2 \cdot 1} : \frac{3}{2} + i \frac{3}{2}

X = \frac{- ( - 3 ) - 3 i}{2 \cdot 1} : \frac{3}{2} - i \frac{3}{2}

The solutions to the quadratic equation are:

X = \frac{3}{2} + i \frac{3}{2}, X = \frac{3}{2} - i \frac{3}{2}

81 u^{2} v

- \frac{1}{8} - \frac{1}{2}

(- 5)^{2} + 3^{2} = x^{2}

x^{2} + 2 x - 16 = 0

∣ x - 52 ∣ \leq 0.02

What are the solutions to the equation X^2=3(X-1) ?
The solutions to the equation X^2=3(X-1) are X= 3/2+i(sqrt(3))/2 ,X= 3/2-i(sqrt(3))/2
Find the zeros of X^2=3(X-1)
The zeros of X^2=3(X-1) are X= 3/2+i(sqrt(3))/2 ,X= 3/2-i(sqrt(3))/2