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What is the positive value of X in the solution set of the equation

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1 Answer

This is not a factorable equation, thus you can solve it using either completion of the square or the quadratic formula.  Completion of the square is actually easier but many students are not skilled at this math.

x + 4x -36= 0           set the equation equal to zero

x+ 4x = 36           move the 36 to the right sige of the equation


x2  + 4x +4  =  36 + 4   add four to each side of the equation. 4 is equal to one half the x coefficient squared.  This makes the left side a perfect square and balance the equation by adding 4 to both sides.

(x + 2)2   =  40           Complete the square

x + 2  = ± (40)½   take the square root of both sides (note the ± symbol)

x = -2 ±    2(10)½


thus the positive answer is -2 + 2(10)½  or minus two plus 2 times the square root of 10