How do you solve $2(x-5)^2=3$ ?

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Answer 1 · 2015-08-21T10:05:43

$x = 5 +- sqrt(6)/2$

The first thing you need to do is isolate $(x-5)^2$ on one side of the equation by dividing both sides by $2$ .

$(color(red)(cancel(color(black)(2))) * (x-5)^2)/color(red)(cancel(color(black)(2))) = 3/2$

$(x-5)^2 = 3/2$

Now you need to take the square root of both sides

$sqrt((x-5)^2) = sqrt(3/2)$

$x-5 = +- sqrt(3)/sqrt(2)$

Rationalize the denominator by multiplying the fraction by $1 = sqrt(2)/sqrt(2)$ to get

$x-5 = +- (sqrt(3) * sqrt(2))/(sqrt(2) * sqrt(2)) = +- sqrt(6)/2$

Finally, isolate $x$ on one side by adding $5$ to both sides of the equation

$x - color(red)(cancel(color(black)(5))) + color(red)(cancel(color(black)(5))) = 5 +- sqrt(6)/2$

$x_(1,2) = 5 +- sqrt(6)/2$

This equation will thus have two solutions,

$x_1 = color(green)(5 + sqrt(6)/2)" "$ or $" "x_2 = color(green)(5 - sqrt(6)/2)$

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