How do you solve x^2 + 9x = -7 graphically and algebraically?

2 Answers
Aug 11, 2017

x approx -0.86 or -8.14

Explanation:

x^2+9x =-7

x^2+9x+7=0

Algebraic Solution:

This is a quadratic eqation of the form: ax^2+bx+c=0

The quadratic formula states:

x=(-b+-sqrt(b^2-4ac))/(2a)

Hence, x= (-9+-sqrt(9^2-4*1*7))/(2*1)

=(-9+-sqrt(81-28))/2

= (-9+-sqrt(53))/2

approx (-9+-7.28)/2

approx -4.5+-3.64

Hence, x approx -0.86 or -8.14

Graphical Solution:

To find the zeros of f(x) = x^2+9x+7 we plot f(x) and find the x-intercepts. As below:

graph{x^2+9x+7 [-28.87, 28.85, -14.44, 14.43]}

As can be seen, the x-intercepts of f(x) are approx -0.86 and -8.14

Hence, this is the graphical solution to the given equation.

Aug 11, 2017

x=(-9 +- sqrt(53))/2

Explanation:

x^2+9x=-7
x^2 + 9x + 7 = 0
x=(-b +- sqrt(b^2 - 4ac))/(2a)
x=(-(9) +- sqrt((9)^2 - 4(1)(7)))/(2(1))
x=(-9 +- sqrt(53))/2

Solving the equation graphically would be inefficient, since the algebraic method is required to use the graphical method. However, if you are given a graph with the exact value of the x-intercepts, the x-intercepts will be the solutions to the equation.