Questions: Solve the equation by the square root property. 2 x^2+3=23

Transcript text: Question list Solve the equation by the square root property. \[ 2 x^{2}+3=23 \]

Solution

Solution Steps

To solve the equation \(2x^2 + 3 = 23\) using the square root property, follow these steps:

Isolate the \(x^2\) term by subtracting 3 from both sides.
Divide both sides by 2 to solve for \(x^2\).
Take the square root of both sides to solve for \(x\), remembering to consider both the positive and negative roots.

Step 1: Isolate the \(x^2\) term

Given the equation: \[ 2x^2 + 3 = 23 \] Subtract 3 from both sides: \[ 2x^2 = 20 \]

Step 2: Solve for \(x^2\)

Divide both sides by 2: \[ x^2 = 10 \]

Step 3: Take the square root of both sides

Take the square root of both sides, considering both the positive and negative roots: \[ x = \pm \sqrt{10} \] Approximating \(\sqrt{10}\) to four significant digits: \[ \sqrt{10} \approx 3.162 \]

Final Answer

\[ \boxed{x = \pm \sqrt{10}} \]

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