SOLUTION: Find all possible solutions. Give your answers in increasing order. Give your answers to the nearest thousandth. \sqrt{1 x + 4} + 3 = 8 x

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find all possible solutions. Give your answers in increasing order. Give your answers to the nearest thousandth. \sqrt{1 x + 4} + 3 = 8 x      Log On


   

Question 910356: Find all possible solutions. Give your answers in increasing order. Give your answers to the nearest thousandth.

\sqrt{1 x + 4} + 3 = 8 x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B4%29%2B3=8x
sqrt%28x%2B4%29=8x-3
x%2B4=%288x-3%29%5E2
x%2B4=64x%5E2-48x%2B9
64x%5E2-49x%2B5=0
Complete the square.
64%28x%5E2-%2849%2F64%29x%29%2B5=0
64%28x%5E2-%2849%2F64%29x%2B%2849%2F128%29%5E2%29%2B5=64%2849%2F128%29%5E2
64%28x-49%2F128%29%5E2%29=64%2849%2F128%29%5E2-5
64%28x-49%2F128%29%5E2%29=2401%2F256-1280%2F256
64%28x-49%2F128%29%5E2%29=1121%2F256
%28x-49%2F128%29%5E2=1121%2F16384
x-49%2F128=0+%2B-+sqrt%281121%2F16384%29
x=49%2F128+%2B-+sqrt%281121%29%2F128
x=%2849+%2B-+sqrt%281121%29%29%2F128
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Graphing the function,sqrt%28x%2B4%29%2B3-8x,
graph%28300%2C300%2C-2%2C2%2C-2%2C2%2Csqrt%28x%2B4%29%2B3-8x%29
The two x values are approximately x=0.644 and x=0.121.
As you see, only the x=0.644 solution actually solves the problem.
x=%2849+%2B+sqrt%281121%29%29%2F128