# SOLUTION: the square root of (3x+10) = 1 + the square root of (2x+5)

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 Question 31046This question is from textbook Algebra 2, Student Edition : the square root of (3x+10) = 1 + the square root of (2x+5)This question is from textbook Algebra 2, Student Edition Found 2 solutions by Cintchr, ikdeep:Answer by Cintchr(481)   (Show Source): You can put this solution on YOUR website! square both sides foil the right side F: O: I: L: combine like terms Move everything AWAY from the sqrt divide all parts by 2 square both sides move everything to the left side This is the difference of two squares. and solve for x in both equations and and Answer by ikdeep(226)   (Show Source): You can put this solution on YOUR website!My earlier solution is incorrect ,,kindly study this one ,,, the square root of (3x+10) = 1 + the square root of (2x+5) on squaring both sdes we get....... (3x+10) = [1 + the square root of (2x+5)]^2 O n RHS we apply fromula (a+b)^2 = (a)^2 + (b)^2 + 2(a)(b) here a = 1 and b = the square root of (2x+5).. on applying formala we get ... (3x+10)=(1)^2 + [the square root of (2x+5)]^2 + 2(1)(the square root of (2x+5) on solving RHS we get... 3x+10 = 1 + 2x + 5 + 2 (1)(the square root of (2x+5) 3x+10 = 2x + 6 + 2 (1)(the square root of (2x+5) taking together the like variables we get..... 3x - 2x + 10 - 6 = 2(the square root of (2x+5) x + 4 = 2(the square root of (2x+5) again squaring both sides we get (x + 4)^2 = [2(the square root of (2x+5)]^2 now we apply the earlier fromula on LHS i.e (a+b)^2 = (a)^2 + (b)^2 + 2(a)(b) here a = x and b = 4 on applying formula we get... (x)^2 + (4)^2 + 2(x)(4) = [2(the square root of (2x+5)]^2 x^2 + 16 + 8x = 4(2x+5) x^2 + 16 + 8x = 8x+ 20 subtract 8x from both sides ,,we get x^2 + 16 = 20 subtract 16 from both sides ,,we get x^2 = 4 taking square root of both sides we get.. either x = 2 0r x = -2 Now if you want to verify you answer ,,,you can put the values of x in the given equation and if you get LHS=RHS,,,this means that you answer is correct.. hope this will help you Please feel free to revert back for any further queries.