How do you solve using the completing the square method $x^2 - 4x + 4 = 100$ ?

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Answer 1 · 2017-09-05T07:41:50

$x=12, " or "-8$

$x^2-4x+4=100$

$=>x^2+4x=100-4=96$

$x^2-4x=96$

take the coefficient of $x$ half it , square it and add and subtract to $LHS$

$x^2-4x+(2)^2-(2)^2=96$

$color(red)(x^2-4x+(2)^2)-(2)^2=96$

the terms in red forma perfect square

$color(red)((x-2)^2)-4=96$

now solve for $x$

$(x-2)^2=96+4=100$

$x-2=+-sqrt100$

$x-2=+-10$

$:x=+10+2, "or "x=-10+2$

$:.x=12, " or "-8$

How do you solve using the completing the square method x^2 - 4x + 4 = 100 x^2 - 4x + 4 = 100?