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WILL GIVE BRAINLIEST
Solve x2 + 4x − 4 = 0.
x equals the quantity of negative 2 plus or minus square root 16 all over 2
x equals negative 4 plus or minus square root 2
x equals negative 2 plus or minus 2 square root 2
x equals the quantity of 4 plus or minus square root 18 all over 2

Respuesta :

kudzordzifrancis

ANSWER

[tex]x=-2\pm 2\sqrt{2}[/tex]


EXPLANATION

Given:

[tex]x^2+4x-4=0[/tex]

We complete the square as follows;


Add 4 to both sides of the equation:


[tex]x^2+4x=4[/tex]


Add half the coefficient of [tex]x[/tex] to both sides of the equation.


[tex]x^2+4x+(2)^2=4+(2)^2[/tex]


The Left Hand Side of the equation is now a perfect square.


[tex](x+2)^2=4+4[/tex]



[tex](x+2)^2=8[/tex]

Take the square root of both sides

[tex]x+2=\pm \sqrt{8}[/tex]



[tex]x=-2\pm 2\sqrt{2}[/tex]


Hence the correct answer is option C





lublana

Given equation is [tex]x^2+4x-4=0[/tex]

compare with [tex]ax^2+bx+c=0[/tex]

we get: a=1, b=4, c=-4

plug these values into quadratic formula:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-4 \pm \sqrt{4^2-4(1)(-4)}}{2(1)}[/tex]

[tex]x=\frac{-4 \pm \sqrt{16-4(-4)}}{2}[/tex]

[tex]x=\frac{-4 \pm \sqrt{16+16}}{2}[/tex]

[tex]x=\frac{-4 \pm \sqrt{32}}{2}[/tex]

[tex]x=\frac{-4 \pm 4\sqrt{2}}{2}[/tex]

[tex]x=-2 \pm 2\sqrt{2}[/tex]

Hence finall answer is:

[tex]x=-2+2\sqrt{2}[/tex] and [tex]x=-2-2\sqrt{2}[/tex]

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