SOLUTION: {{{ 2x=sqrt(8-4x) }}}

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Question 1207452: +2x=sqrt%288-4x%29+
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+2x=sqrt%288-4x%29+....square both sides
+4x%5E2=8-4x+....divide by 4
+x%5E2=2-x+
+x%5E2%2Bx-2=0+...factor
+x%5E2%2B2x-x-2=0+
+%28x%5E2%2B2x%29-%28x%2B2%29=0+
+x%28x%2B2%29-%28x%2B2%29=0+
+%28x-1%29%28x%2B2%29=0+

solutions:
x=1
x=-2

verify solutions:
+2%2A1=sqrt%288-4%2A1%29+=>+2=2+=> true
+2%2A%28-2%29=sqrt%288-4%2A%28-2%29%29+=>+-4=4=> false

so, your solution is x=1

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2C+sqrt%288-4x%29%29+


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

As the other tutor mentions, the only solution is x = 1.

The other value x = -2 is extraneous.

Here's the graph mentioned.
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2C+sqrt%288-4x%29%29+

Let's reflect the square root curve over the x axis to handle y+=+-sqrt%288-4x%29
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2C+sqrt%288-4x%29%2C-sqrt%288-4x%29%29+
Notice the new intersection point (-2,-4) which is the intersection of y = 2x and y = -sqrt(8-4x)

So if we were allowed to plot the plus minus of sqrt%288-4x%29 then we'd get two solutions for x.
However, we only plot the positive version.