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

The solutions to the equation (3X-1)^2+X(X-3)=-1 are X= 1/2 ,X= 2/5

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

The zeros of (3X-1)^2+X(X-3)=-1 are X= 1/2 ,X= 2/5

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

X = \frac{1}{2}, X = \frac{2}{5}

Decimal Notation

X = 0.5, X = 0.4

Solution steps

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

Expand

(3 X - 1)^{2} + X (X - 3) : 10 X^{2} - 9 X + 1

10 X^{2} - 9 X + 1 = - 1

Move

1

to the left side

10 X^{2} - 9 X + 2 = 0

Solve with the quadratic formula

X_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 10 \cdot 2}{2 \cdot 10}

(- 9)^{2} - 4 \cdot 10 \cdot 2 = 1

X_{1, 2} = \frac{- ( - 9 ) \pm 1}{2 \cdot 10}

Separate the solutions

X_{1} = \frac{- ( - 9 ) + 1}{2 \cdot 10}, X_{2} = \frac{- ( - 9 ) - 1}{2 \cdot 10}

X = \frac{- ( - 9 ) + 1}{2 \cdot 10} : \frac{1}{2}

X = \frac{- ( - 9 ) - 1}{2 \cdot 10} : \frac{2}{5}

The solutions to the quadratic equation are:

X = \frac{1}{2}, X = \frac{2}{5}

x^{2} - 10 x = x + 12

x^{2} - 2 x = 3

4 z^{2} - 4 z + 9 = 0

x^{2} - \frac{5}{2} x = 0

(19 x - 1)^{2} - 2 (19 x - 1) - 3 = 0

What are the solutions to the equation (3X-1)^2+X(X-3)=-1 ?
The solutions to the equation (3X-1)^2+X(X-3)=-1 are X= 1/2 ,X= 2/5
Find the zeros of (3X-1)^2+X(X-3)=-1
The zeros of (3X-1)^2+X(X-3)=-1 are X= 1/2 ,X= 2/5