What are the solutions to the equation x^2-2(k-3)x+4k=0 ?

The solutions to the equation x^2-2(k-3)x+4k=0 are x=k-3+sqrt(k^2-10k+9),x=k-3-sqrt(k^2-10k+9)

Find the zeros of x^2-2(k-3)x+4k=0

The zeros of x^2-2(k-3)x+4k=0 are x=k-3+sqrt(k^2-10k+9),x=k-3-sqrt(k^2-10k+9)

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x^{2} - 2 (k - 3) x + 4 k = 0

x = k - 3 + k^{2} - 10 k + 9, x = k - 3 - k^{2} - 10 k + 9

Solution steps

x^{2} - 2 (k - 3) x + 4 k = 0

Expand

x^{2} - 2 (k - 3) x + 4 k : x^{2} - 2 k x + 6 x + 4 k

x^{2} - 2 k x + 6 x + 4 k = 0

Write in the standard form

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

x^{2} + (- 2 k + 6) x + 4 k = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 k + 6 ) \pm ( - 2 k + 6 ) ^{2} - 4 \cdot 1 \cdot 4 k}{2 \cdot 1}

Simplify

(- 2 k + 6)^{2} - 4 \cdot 1 \cdot 4 k : 2 k^{2} - 10 k + 9

x_{1, 2} = \frac{- ( - 2 k + 6 ) \pm 2 k ^{2} - 10 k + 9}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 2 k + 6 ) + 2 k ^{2} - 10 k + 9}{2 \cdot 1}, x_{2} = \frac{- ( - 2 k + 6 ) - 2 k ^{2} - 10 k + 9}{2 \cdot 1}

x = \frac{- ( - 2 k + 6 ) + 2 k ^{2} - 10 k + 9}{2 \cdot 1} : k - 3 + k^{2} - 10 k + 9

x = \frac{- ( - 2 k + 6 ) - 2 k ^{2} - 10 k + 9}{2 \cdot 1} : k - 3 - k^{2} - 10 k + 9

The solutions to the quadratic equation are:

x = k - 3 + k^{2} - 10 k + 9, x = k - 3 - k^{2} - 10 k + 9

68.2 = 39.2 t - 4.9 t^{2}

(36 - R)^{2} + (18 - R)^{2} = R^{2}

5 x^{2} - 20 x - 12 = 0

4 x^{2} + x - \frac{1}{16} = 0

9 x^{2} - 6 x + 1 = 0

What are the solutions to the equation x^2-2(k-3)x+4k=0 ?
The solutions to the equation x^2-2(k-3)x+4k=0 are x=k-3+sqrt(k^2-10k+9),x=k-3-sqrt(k^2-10k+9)
Find the zeros of x^2-2(k-3)x+4k=0
The zeros of x^2-2(k-3)x+4k=0 are x=k-3+sqrt(k^2-10k+9),x=k-3-sqrt(k^2-10k+9)