What are the solutions to the equation completesquare 6+4x-x^2 ?

The solutions to the equation completesquare 6+4x-x^2 are -(x-2)^2+10

Find the zeros of completesquare 6+4x-x^2

The zeros of completesquare 6+4x-x^2 are -(x-2)^2+10

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complete the square

6 + 4 x - x^{2}

- (x - 2)^{2} + 10

Solution steps

6 + 4 x - x^{2}

Write in the standard form

a x^{2} + b x + c

- x^{2} + 4 x + 6

Write

- x^{2} + 4 x + 6

in the form:

x^{2} + 2 a x + a^{2}

Factor out

- 1

- (x^{2} - 4 x - 6)

2 a = - 4 : a = - 2

Add and subtract

(- 2)^{2}

- (x^{2} - 4 x - 6 + (- 2)^{2} - (- 2)^{2})

x^{2} + 2 a x + a^{2} = (x + a)^{2}

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

- ((x - 2)^{2} - 6 - (- 2)^{2})

Simplify

- (x - 2)^{2} + 10

\frac{x ^{2}}{3} = 27

7 x^{2} + 21 x + 14 = 0

2 (4 x)^{2} = 128

3 p^{2} + 5 p - 10 = 0

4 x = 21 - x^{2}

What are the solutions to the equation completesquare 6+4x-x^2 ?
The solutions to the equation completesquare 6+4x-x^2 are -(x-2)^2+10
Find the zeros of completesquare 6+4x-x^2
The zeros of completesquare 6+4x-x^2 are -(x-2)^2+10