Solve Using the Square Root Property x^2+53=0

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Trigonometry

$x^{2} + 53 = 0$

Subtract $53$ from both sides of the equation.

$x^{2} = - 53$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- 53}$

The complete solution is the result of both the positive and negative portions of the solution.

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Simplify the right side of the equation.

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Rewrite $- 53$ as $- 1 (53)$ .

$x = \pm \sqrt{- 1 \cdot 53}$

Rewrite $\sqrt{- 1 (53)}$ as $\sqrt{- 1} \cdot \sqrt{53}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{53}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \sqrt{53}$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$x = i \sqrt{53}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - i \sqrt{53}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = i \sqrt{53}, - i \sqrt{53}$

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