Solve x^2 +11x +30 = 0

This is what we call a quadratic equation. To solve, first we need to factorise this equation into two brackets. (x + _ )(x + _) =0To fill the brackets, we need to find 2 numbers that add to 11 and multiply to 30. Let's think about the factors of 30:30 and 115 and 2 10 and 3 5 and 6 Which of these pairs of factors adds to 11? 5 and 6 This gives us: x^2 +11x +30 = (x+5)(x+6) = 0Now, we need to solve. A quadratic equation will always have 2 solutions.(x+5)(x+6)=0 If we multiply 2 numbers together and get the answer 0, this means that at least one of the numbers must be 0. Therefore, x+5=0 and/or x+6=0Let's solve one at a time:x+5=0 We need x by itself on one side of the equation, so minus 5 from both sides of the equation: x= -5x+6=0Minus 6 from both sides of the equation:x=-6We have our 2 solutions: x=-5 and x=-6