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

2 Answers
Aug 11, 2017

Answer:

#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

Answer:

#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.