Answer
$x = 2\sqrt {7}-5$ or $x=-2\sqrt {7}-5$
Work Step by Step
$x^2 + 10x - 3 = 0$
Add $3$ to both sides.
$x^2 + 10x - 3+3 = 0+3$
$x^2 + 10x = 3$
The coefficient of the $x$-term is $10$. Half of $10$ is $5$, and $5^2$ is $25$. Thus, add $25$ to both sides to complete the square.
$x^2 + 10x +25= 3+25$
$(x+5)^2=±\sqrt {28}$
$x+5= ±4\sqrt {7}$
Subtract $5$ to both sides.
$x+5-5= ±2\sqrt {7}-5$
$x= ±2\sqrt {7}-5$
$x = 2\sqrt {7}-5$ or $x=-2\sqrt {7}-5$
