What are the solutions to the equation completesquare 3+x-x^2 ?

The solutions to the equation completesquare 3+x-x^2 are -(x-1/2)^2+13/4

Find the zeros of completesquare 3+x-x^2

The zeros of completesquare 3+x-x^2 are -(x-1/2)^2+13/4

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complete the square

3 + x - x^{2}

- (x - \frac{1}{2})^{2} + \frac{13}{4}

Solution steps

3 + x - x^{2}

Write in the standard form

a x^{2} + b x + c

- x^{2} + x + 3

Write

- x^{2} + x + 3

in the form:

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

Factor out

- 1

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

2 a = - 1 : a = - \frac{1}{2}

Add and subtract

(- \frac{1}{2})^{2}

- (x^{2} - x - 3 + (- \frac{1}{2})^{2} - (- \frac{1}{2})^{2})

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

x^{2} - 1 x + (- \frac{1}{2})^{2} = (x - \frac{1}{2})^{2}

- ((x - \frac{1}{2})^{2} - 3 - (- \frac{1}{2})^{2})

Simplify

- (x - \frac{1}{2})^{2} + \frac{13}{4}

4 x^{2} - 8 x - 10 = 0

6 x^{2} - 10 x = 4

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

2 x - 3 x^{2} = 5

20 (t^{2} + 16) = 320 t

What are the solutions to the equation completesquare 3+x-x^2 ?
The solutions to the equation completesquare 3+x-x^2 are -(x-1/2)^2+13/4
Find the zeros of completesquare 3+x-x^2
The zeros of completesquare 3+x-x^2 are -(x-1/2)^2+13/4