2x²+5|x|=0

To solve the equation \(2x^2 + 5|x| = 0\), we need to consider the absolute value. The expression \(5|x|\) is non-negative because absolute values are always non-negative, and \(2x^2\) is also non-negative since it is a square term multiplied by a positive constant. Thus, the left-hand side of the equation \(2x^2 + 5|x|\) can only equal zero if both terms are individually zero. Therefore, we set each term to zero: 1. **First term:** \[ 2x^2 = 0 \implies x^2 = 0 \implies x = 0 \] 2. **Second term:** \[ 5|x| = 0 \implies |x| = 0 \implies x = 0 \] Both conditions lead to the same solution: \[ x = 0 \] Thus, the only solution to the equation \(2x^2 + 5|x| = 0\) is \[ \boxed{0}. \]