Math

QuestionSolve for xx in the equation x+34=1+32x + 3 \sqrt{4} = 1 + 3 \sqrt{2} and find x+4x + 4.

Studdy Solution

STEP 1

Assumptions1. We are given the equation x+34=1+3x+3 \sqrt{4}=1+3 \sqrt{} . We are asked to find the value of x+4x+4

STEP 2

First, we simplify the equation. We know that 4=2\sqrt{4}=2, so we can substitute this into the equation.
x+4=1+2x+×2=1+2x+ \sqrt{4}=1+ \sqrt{2} \Rightarrow x+ \times2=1+ \sqrt{2}

STEP 3

implify the left side of the equation.
x+6=1+32x+6=1+3 \sqrt{2}

STEP 4

Now, we isolate xx by subtracting6 from both sides of the equation.
x=1+326x=1+3 \sqrt{2} -6

STEP 5

implify the right side of the equation.
x=5+32x=-5+3 \sqrt{2}

STEP 6

Now that we have the value of xx, we can substitute it into the expression x+4x+4 to find its value.
x+4=(5+32)+4x+4=(-5+3 \sqrt{2})+4

STEP 7

implify the expression.
x+4=1+32x+4=-1+3 \sqrt{2}So, x+4=1+32x+4=-1+3 \sqrt{2}.

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