You can put this solution on YOUR website! the roots are -4 and -2/7
this means that x = -4 and x = -2/7
add 4 to both sides of the equation of x = -4 to get:
x + 4 = 0
multiply both sides of the equation of x = -2/7 to get:
7x = -2
add 2 to both sides of the equation of 7x = -2 to get:
7x + 2 = 0
(x + 4) is one of the factors of the quadratic equation and (7x + 2) is the other factor.
multiply these factors together and you get:
(x + 4) * (7x + 2) = x * (7x + 2) + 4 * (7x + 2) = 7x^2 + 2x + 28x + 8
combine like terms and order the terms in descending order of degree and you get:
7x^2 + 30x + 8
set this expression equal to 0 and you get:
7x^2 + 30x + 8 = 0
set this expression equal to y and you get:
7x^2 + 30x + 8 = y
the equation of y = 7x^2 + 30x + 8 is factored by setting y equal to 0 to get 7x^2 + 30x + 8 = 0
it is then factored to get (x + 4) * (7x + 2) = 0
the roots of this equation are x = -4 and x = -2/7
if they are roots, then the equation will be equal to 0 when you replace x with -4 and when you replace x with -2/7.
when you replace x with -4, the equation of y = 7x^2 + 30x + 8 becomes y = 7 * (-4)^2 + 30 * -4 + 8 which becomes y = 7 * 16 - 120 + 8 which becomes y = 112 - 120 + 8 which becomes y = 0, confirming that x = -4 is a root.
when you replace x with -2/7, the equation of y = 7x^2 + 30x + 8 becomes y = 7 * (-2/7)^2 + 30 * -2/7 + 8 which becomes y = 7 * 4/49 + 30 * -2/7 + 8 which becomes y = 4/7 - 60/7 + 8 which becomes y = -56/7 + 8 which becomes y = -8 + 8 which becomes y = 0, confirming that x = -2/7 is also a root.
if you graph the equation of y = 7x^2 + 30x + 4, you will get the following graph.
the graph crosses the x-axis at x = -4 and x = -.286
note that -2/7 = -.286 rounded to 3 decimal places.
