What are the solutions to the equation completesquare 4x^2-36x+81 ?

The solutions to the equation completesquare 4x^2-36x+81 are 4(x-9/2)^2

Find the zeros of completesquare 4x^2-36x+81

The zeros of completesquare 4x^2-36x+81 are 4(x-9/2)^2

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complete the square

4 x^{2} - 36 x + 81

4 (x - \frac{9}{2})^{2}

Solution steps

4 x^{2} - 36 x + 81

Write

4 x^{2} - 36 x + 81

in the form:

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

Factor out

4

4 (x^{2} - 9 x + \frac{81}{4})

2 a = - 9 : a = - \frac{9}{2}

Add and subtract

(- \frac{9}{2})^{2}

4 (x^{2} - 9 x + \frac{81}{4} + (- \frac{9}{2})^{2} - (- \frac{9}{2})^{2})

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

x^{2} - 9 x + (- \frac{9}{2})^{2} = (x - \frac{9}{2})^{2}

4 ((x - \frac{9}{2})^{2} + \frac{81}{4} - (- \frac{9}{2})^{2})

Simplify

4 (x - \frac{9}{2})^{2}

1.36 x^{2} + 27.8 x + 304 = 500

(400 + j^{1000}) I^{2} - j^{90} I^{1} = 0

49 x^{2} - 60 = 0

x^{2} + 15 = 8

x^{2} - 4 x + 87 = 0

What are the solutions to the equation completesquare 4x^2-36x+81 ?
The solutions to the equation completesquare 4x^2-36x+81 are 4(x-9/2)^2
Find the zeros of completesquare 4x^2-36x+81
The zeros of completesquare 4x^2-36x+81 are 4(x-9/2)^2