# How do you solve x^2-4<=0?

Aug 30, 2016

-2 ≤ x ≤2

#### Explanation:

Write as a quadratic equation and solve, and then select test points.

${x}^{2} - 4 = 0$

$\left(x + 2\right) \left(x - 2\right) = 0$

$x = - 2 \mathmr{and} 2$

Usually, we choose one point inside the parabola and another outside

The x-intercepts of the parabola are $x = \pm 2$, so let the test point on the exterior be $x = - 4$ and the point on the interior be $x = 1$.

Test point 1: $x = - 4$

-4^2 - 4 <=^?0

$12 \cancel{\le} 0$

Hence, by deduction, the interval of solution is -2 ≤ x ≤ 2. Or, in other words, the inside of the parabola is shaded.

Hopefully this helps!