What are the solutions to the equation completesquare x^2+1/2 x-4 ?

The solutions to the equation completesquare x^2+1/2 x-4 are (x+1/4)^2-65/16

Find the zeros of completesquare x^2+1/2 x-4

The zeros of completesquare x^2+1/2 x-4 are (x+1/4)^2-65/16

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complete the square

x^{2} + \frac{1}{2} x - 4

(x + \frac{1}{4})^{2} - \frac{65}{16}

Solution steps

x^{2} + \frac{1}{2} x - 4

Write in the standard form

a x^{2} + b x + c

x^{2} + \frac{x}{2} - 4

Write

x^{2} + \frac{x}{2} - 4

in the form:

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

2 a = \frac{1}{2} : a = \frac{1}{4}

Add and subtract

(\frac{1}{4})^{2}

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

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

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

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

Simplify

(x + \frac{1}{4})^{2} - \frac{65}{16}

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

- x^{2} + 10 x = 16

4 x^{2} + 2 x - 12 = 0

y^{2} + y

x, x^{2} - 4 x = 0

What are the solutions to the equation completesquare x^2+1/2 x-4 ?
The solutions to the equation completesquare x^2+1/2 x-4 are (x+1/4)^2-65/16
Find the zeros of completesquare x^2+1/2 x-4
The zeros of completesquare x^2+1/2 x-4 are (x+1/4)^2-65/16