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

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]