Question 692113
Take the square root of both sides
{{{(x+4)^2=3/25}}}
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{{{sqrt(x+4)^2}}} = +/-{{{sqrt(3/25)}}}
x+4 = +/- {{{sqrt(3)/5}}}
{{{highlight_green(x = -4 +-sqrt(3)/5)}}}
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Two Solutions
x = {{{-4+sqrt(3)/5}}}
x = {{{-4-sqrt(3)/5}}}
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Alternatively,
(x+4)(x+4)={{{3/25}}}
{{{x^2 + 8x + 16 = 3/25}}} ==> multiply by 25
25({{{x^2 + 8x + 16 = 3/25}}})
{{{25x^2 + 200x + 400 = 3}}}
{{{25x^2 + 200x + 397 - 0}}}
Apply the quadratic formula
x = {{{(-200+-sqrt(200^2-4(25)(397)))/(2*25)}}}
x = {{{(-200+-sqrt(40000-39700))/50}}}
x = {{{(-200+-sqrt(300))/50}}}
x = {{{(-200+-10sqrt(3))/50}}}
x = {{{-4+-sqrt(3)/5}}}
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In short, you erred within the multiplication of the equation by 25
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