Solve for x square root of x^2+15-4=0

Problem

√(,x^2+15)−4=0

Solution

1. Isolate the radical term by adding 4 to both sides of the equation.

√(,x^2+15)=4

2. Square both sides of the equation to eliminate the square root.

(√(,x^2+15))^2=4^2

x^2+15=16

3. Isolate the x^2 term by subtracting 15 from both sides.

x^2=1

4. Solve for x by taking the square root of both sides, remembering to include both the positive and negative roots.

x=±√(,1)

x=±1

5. Verify the solutions by substituting them back into the original equation. For x=1 or x=−1 x^2=1 so √(,1+15)−4=√(,16)−4=4−4=0 Both solutions are valid.

Final Answer

√(,x^2+15)−4=0⇒x=1,−1

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