Question

How to solve (4x-7)^2=44

Answer 1

Well, First I would write it in the expanded form which is 16x^2-56x+49=44 then i would reorder my terms to  49+-56x+16^2=4 then  solve for x so it would be 49+ -44 + -56 +16^2=44+ -44 then combine the like terms 49+ -44=5
 5+-56x+16x^2= 44+-44 would turn into 
44+ -44 =0 
5+ -56+16^2=0 
i would do the squaring and  divide all the terms by 16 the coefficient of the squared term:
divide each side by 16 so
0.3125+ -3.5x+ x^2=0
move the constant to the right  
add -0.3125 to each side  0.3125 + -3.5x + -0.3125 + x2 = 0 + -0.3125 then reorder 
0.3125 + -0.3125 + -3.5x + x2 = 0 + -0.3125
0.3125 + -0.3125 + -3.5x + x2 = 0 + -0.3125

then 

x + -1.75 = 1.658312395 Simplifying x + -1.75 = 1.658312395 Reorder the terms: -1.75 + x = 1.658312395 Solving -1.75 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.658312395 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.658312395 + 1.75 x = 1.658312395 + 1.75 Combine like terms: 1.658312395 + 1.75 = 3.408312395 x = 3.408312395 Simplifying x = 3.408312395

then 

x + -1.75 = -1.658312395 Simplifying x + -1.75 = -1.658312395 Reorder the terms: -1.75 + x = -1.658312395 Solving -1.75 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.658312395 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.658312395 + 1.75 x = -1.658312395 + 1.75 Combine like terms: -1.658312395 + 1.75 = 0.091687605 x = 0.091687605 Simplifying x = 0.091687605

and finally your solution is x=3.408312395 and x=0.091687605

or another  way to write it is 

x=\frac{1}{4}(7-2 \sqrt{11} ) [/tex]    
x=\frac{1}{4}(7+2 \sqrt{11} ) [/tex]