Questions: Solve the following equation for (x) by using a graphing calculator. Round your answers to 3 decimal places. [ x+2=sqrt4 x+7 ] [ x= ]

Transcript text: Solve the following equation for $x$ by using a graphing calculator. Round your answers to 3 decimal places. \[ x+2=\sqrt{4 x+7} \] \[ x= \]

Solution

Solution Steps

Step 1: Rearranging the Equation

Start with the original equation: \[ x + 2 = \sqrt{4x + 7} \] Rearrange it to isolate the square root: \[ x + 2 - \sqrt{4x + 7} = 0 \]

Step 2: Defining the Function

Define the function based on the rearranged equation: \[ f(x) = x + 2 - \sqrt{4x + 7} \] We need to find the value of $ x $ for which $ f(x) = 0 $.

Step 3: Finding the Root

Using a numerical method, we find the root of the function $ f(x) $. The solution yields: \[ x \approx 1.732 \] This value is rounded to three decimal places as required.

Final Answer

$\boxed{x \approx 1.732}$

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