Solve x^2geq15-78+356

$$x ^ { 2 } \geq 15 - 78 + 356$$

Solve for x

$$x\in (-\infty,-\sqrt{293}]\cup [\sqrt{293},\infty)$$

Solution Steps

Subtract 78 from 15 to get -63.

$$x^{2}\geq -63+356$$

Add -63 and 356 to get 293.

$$x^{2}\geq 293$$

Calculate the square root of 293 and get \sqrt{293}. Rewrite 293 as \left(\sqrt{293}\right)^{2}.

$$x^{2}\geq \left(\sqrt{293}\right)^{2}$$

Inequality holds for |x|\geq \sqrt{293}.

$$|x|\geq \sqrt{293}$$

Rewrite |x|\geq \sqrt{293} as x\leq -\sqrt{293}\text{; }x\geq \sqrt{293}.

$$x\leq -\sqrt{293}\text{; }x\geq \sqrt{293}$$