What are the solutions to the equation completesquare-x^2-3x-1 ?

The solutions to the equation completesquare-x^2-3x-1 are -(x+3/2)^2+5/4

Find the zeros of completesquare-x^2-3x-1

The zeros of completesquare-x^2-3x-1 are -(x+3/2)^2+5/4

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complete the square

- x^{2} - 3 x - 1

- (x + \frac{3}{2})^{2} + \frac{5}{4}

Solution steps

- x^{2} - 3 x - 1

Write

- x^{2} - 3 x - 1

in the form:

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

Factor out

- 1

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

2 a = 3 : a = \frac{3}{2}

Add and subtract

(\frac{3}{2})^{2}

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

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

x^{2} + 3 x + (\frac{3}{2})^{2} = (x + \frac{3}{2})^{2}

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

Simplify

- (x + \frac{3}{2})^{2} + \frac{5}{4}

2 (x - 3)^{2} = 50

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

4 x^{2} + 2 x = 13

11 x^{2} - 4 x + 11 = 0

X^{2} - 7 X - 18 = 0

What are the solutions to the equation completesquare-x^2-3x-1 ?
The solutions to the equation completesquare-x^2-3x-1 are -(x+3/2)^2+5/4
Find the zeros of completesquare-x^2-3x-1
The zeros of completesquare-x^2-3x-1 are -(x+3/2)^2+5/4