Question

solve the quadratic equation by completing the square
x^2+10x+19=0

Answer 1

@hartnn @zepdrix @zephyr141 @suckerofmath

Answer 2

ok first you need to start by putting the values without a variable on the right side of the equation. \[x^2+10x=-19\] then you take half of the number paired with the x and square that result and add to both sides of the equation like so \[x^2+10x+\left( \frac{ 10 }{ 2 } \right)^2=-19+\left( \frac{ 10 }{ 2 } \right)^2\] and you will have \[x^2+10x+25=6\] now this is in the form of a perfect square and easy to do since we know what the square of 25 is.\[(x+5)^2=6\] now at this point you take the square root of both sides to allow x to be easily solved. remember that the radical here needs a positive and a negative before it\[x+5=\pm \sqrt{6}\] and now the result is simply \[x=-5+\sqrt{6}\] or \[x=-5-\sqrt{6}\]