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

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

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

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

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complete the square

x^{2} - x - 1

(x - \frac{1}{2})^{2} - \frac{5}{4}

Solution steps

x^{2} - x - 1

Write

x^{2} - x - 1

in the form:

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

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

Add and subtract

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

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

Simplify

(x - \frac{1}{2})^{2} - \frac{5}{4}

(x - 5)^{2} = - 25

2 x^{2} - 7 x + 5

12 x^{2} - 30 x = 0

4 x^{2} - 1 = 15

n^{2} - 20 n + 100 = 40

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