What are the solutions to the equation (x-2)^2=3x-4 ?

The solutions to the equation (x-2)^2=3x-4 are x=(7+sqrt(17))/2 ,x=(7-sqrt(17))/2

Find the zeros of (x-2)^2=3x-4

The zeros of (x-2)^2=3x-4 are x=(7+sqrt(17))/2 ,x=(7-sqrt(17))/2

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(x - 2)^{2} = 3 x - 4

x = \frac{7 + 17}{2}, x = \frac{7 - 17}{2}

Decimal Notation

x = 5.56155 \dots, x = 1.43844 \dots

Solution steps

(x - 2)^{2} = 3 x - 4

Expand

(x - 2)^{2} : x^{2} - 4 x + 4

x^{2} - 4 x + 4 = 3 x - 4

Move

4

to the left side

x^{2} - 4 x + 8 = 3 x

Move

3 x

to the left side

x^{2} - 7 x + 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 1 \cdot 8}{2 \cdot 1}

(- 7)^{2} - 4 \cdot 1 \cdot 8 = 17

x_{1, 2} = \frac{- ( - 7 ) \pm 17}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 7 ) + 17}{2 \cdot 1}, x_{2} = \frac{- ( - 7 ) - 17}{2 \cdot 1}

x = \frac{- ( - 7 ) + 17}{2 \cdot 1} : \frac{7 + 17}{2}

x = \frac{- ( - 7 ) - 17}{2 \cdot 1} : \frac{7 - 17}{2}

The solutions to the quadratic equation are:

x = \frac{7 + 17}{2}, x = \frac{7 - 17}{2}

x^{2} - 2 x^{2} - 4 x + 8 = 0

2 x^{2} + 6 x = 31

5 (2 x - 4) = - 4 (x^{2})

(x + 1) (x - 3) = 2

4 = 2 x^{2} + 3

What are the solutions to the equation (x-2)^2=3x-4 ?
The solutions to the equation (x-2)^2=3x-4 are x=(7+sqrt(17))/2 ,x=(7-sqrt(17))/2
Find the zeros of (x-2)^2=3x-4
The zeros of (x-2)^2=3x-4 are x=(7+sqrt(17))/2 ,x=(7-sqrt(17))/2