Question 29360
{{{sqrt(x - 2) = 4}}}
square both sides
{{{x - 2 = 16}}}
{{{x = 18}}}
check
{{{sqrt(x - 2) = 4}}}
{{{sqrt(18 - 2) = 4}}}
{{{sqrt(16) = 4}}}
this is true- one of the square roots of 16 is 4, the othewr is -4
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{{{2 * sqrt(x +3) = 10}}}
square both sides
{{{4 * (x + 3) = 100}}}
{{{x + 3  = 100 / 4}}}
{{{x = 25 - 3}}}
{{{x = 22}}}
check
{{{2 * sqrt(x +3) = 10}}}
{{{2 * sqrt(22 +3) = 10}}}
{{{sqrt(25) = 10/2}}}
{{{5 = 5}}}
true, one of the square roots of 25 is +5, the other  is -5
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{{{x = sqrt(x + 6)}}}
square both sides
{{{x^2 = x + 6}}}
{{{x^2 - x - 6 = 0}}}
solve for x
{{{(x - 3) * (x + 2) = 0}}}
x = 3
x = -2
check
{{{x = sqrt(x + 6)}}}
{{{3 = sqrt(3 + 6)}}}
{{{3 = sqrt(9)}}}
true- one of the square roots of 9 is +3, the other is -3
{{{-2 = sqrt(-2 + 6)}}}
{{{-2 = sqrt(4)}}}
true one of the square roots of 4 is -2, the other is +2
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{{{sqrt(x) + 1 = 5}}}
{{{sqrt(x) = 4}}}
square both sides
{{{x = 16}}}
check
{{{sqrt(x) + 1 = 5}}}
{{{sqrt(16) + 1 = 5}}}
{{{4 + 1 = 5}}}
true- one of the square roots of 16 is 4, the other is -4