Please help!!!!
(square root of x) + 3 = square root of (x+12)
sqrt ( x ) + 3 = sqrt ( x + 12 ) Subtract 3 from both sides:
sqrt ( x ) + 3 - 3 = sqrt ( x + 12 ) - 3
sqrt ( x ) = sqrt ( x + 12 ) - 3
Square both sides :
[ sqrt ( x ) ] ^ 2 = [ sqrt ( x + 12 ) ] ^ 2
- 2 * sqrt ( x + 12 ) * 3 + 3 ^ 2
x = x + 12 - 6 sqrt ( x + 12 ) + 9
x = x - 6 sqrt ( x + 12 ) + 21
Add 6 sqrt ( x + 12 ) from both sides:
x + 6 sqrt ( x + 12 ) = x - 6 sqrt ( x + 12 ) + 21 + 6 sqrt ( x + 12 )
x + 6 sqrt ( x + 12 ) = x + 21 Subtract x from both sides:
x + 6 sqrt ( x + 12 ) - x = x + 21 - x
6 sqrt ( x + 12 ) = 21 Square both sides
6 ^ 2 * [ sqrt ( x + 12 ) ] ^ 2 = 21 ^ 2
36 ( x + 12 ) = 441
36 x + 36 * 12 = 441
36 x + 432 = 441 Subtract 432 from both sides
36 x + 432 - 432 = 441 - 432
36 x = 9 Divide both sides by 36
x = 9 / 36 = 9 / ( 9 * 4 ) = 1 / 4
x = 1 / 4
Remark :
( a - b ) ^ 2 = a ^ 2 - 2 * a * b + b ^ 2
To solve the equation (square root of x) + 3 = (square root of (x+12)), we need to isolate the square root terms on one side and simplify the equation step by step. Here's how you can do it:
Step 1: Start by subtracting 3 from both sides of the equation:
(square root of x) = (square root of (x+12)) - 3
Step 2: To eliminate the square root on the right side, square both sides of the equation:
((square root of x))^2 = ((square root of (x+12)) - 3)^2
Step 3: Simplify the equation by squaring both sides:
x = (x+12) - 6(square root of (x+12)) + 9
Step 4: Combine like terms and move all terms with x to one side of the equation:
x - x - 12 + 6(square root of (x+12)) = 9
Step 5: Simplify further:
6(square root of (x+12)) = 9 + 12
Step 6: Continue simplifying:
6(square root of (x+12)) = 21
Step 7: Divide both sides of the equation by 6:
(square root of (x+12)) = 21/6
Step 8: Simplify the right side fraction:
(square root of (x+12)) = 7/2
Step 9: Square both sides to eliminate the square root:
(square root of (x+12))^2 = (7/2)^2
Step 10: Simplify:
x + 12 = 49/4
Step 11: Subtract 12 from both sides to isolate x:
x = 49/4 - 12
Step 12: Convert the fraction on the right side to a common denominator:
x = 49/4 - 48/4
Step 13: Combine the fractions:
x = 1/4
Therefore, the solution to the equation (square root of x) + 3 = (square root of (x+12)) is x = 1/4.