What are the solutions to the equation (x-1)^2+(7-2x)^2=10 ?

The solutions to the equation (x-1)^2+(7-2x)^2=10 are x=4,x=2

Find the zeros of (x-1)^2+(7-2x)^2=10

The zeros of (x-1)^2+(7-2x)^2=10 are x=4,x=2

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(x - 1)^{2} + (7 - 2 x)^{2} = 10

x = 4, x = 2

Solution steps

(x - 1)^{2} + (7 - 2 x)^{2} = 10

Expand

(x - 1)^{2} + (7 - 2 x)^{2} : 5 x^{2} - 30 x + 50

5 x^{2} - 30 x + 50 = 10

Move

10

to the left side

5 x^{2} - 30 x + 40 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 30 ) \pm ( - 30 ) ^{2} - 4 \cdot 5 \cdot 40}{2 \cdot 5}

(- 30)^{2} - 4 \cdot 5 \cdot 40 = 10

x_{1, 2} = \frac{- ( - 30 ) \pm 10}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 30 ) + 10}{2 \cdot 5}, x_{2} = \frac{- ( - 30 ) - 10}{2 \cdot 5}

x = \frac{- ( - 30 ) + 10}{2 \cdot 5} : 4

x = \frac{- ( - 30 ) - 10}{2 \cdot 5} : 2

The solutions to the quadratic equation are:

x = 4, x = 2

(x + 5) (2 x - 3) = 2 (x + 1)

(3 x - 2) (x + 1) = 8 x - 3

3 x^{2} + 5 x - 28 = 0

(1 + 5 x)^{2} = (4 x - 1) 2^{2} + 9 x (x - 2)

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

What are the solutions to the equation (x-1)^2+(7-2x)^2=10 ?
The solutions to the equation (x-1)^2+(7-2x)^2=10 are x=4,x=2
Find the zeros of (x-1)^2+(7-2x)^2=10
The zeros of (x-1)^2+(7-2x)^2=10 are x=4,x=2