SOLUTION: Solve the following equation for ALL SOLUTIONS
x^2-10x= -9
using the QUADRATIC FORMULA and INCLUDING AT LEAST THE FIRST TWO MIDDLE STEPS
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Question 264878: Solve the following equation for ALL SOLUTIONS
x^2-10x= -9
using the QUADRATIC FORMULA and INCLUDING AT LEAST THE FIRST TWO MIDDLE STEPS
Found 2 solutions by mananth, Theo:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Solve the following equation for ALL SOLUTIONS
x^2-10x= -9
using the QUADRATIC FORMULA and INCLUDING AT LEAST THE FIRST TWO MIDDLE STEPS
x^2-10x+9=0
X^2-9x-x+9=0
x(x-9)- 1(x-9)=0
(x-9)(x-1)=0
x= 9 0r 1
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
equation is:
x^2-10x= -9
add 9 to both sides of this equation to get it into standard form.
you get:
x^2 - 10x + 9 = 0
standard form of the quadratic equation is ax^2 + bx + c = 0
this means that:
a = 1
b = -10
c = 9
quadratic formula is:
x = (-b +- sqrt(b^2-4ac))/(2a)
this becomes:
(-(-10) +- sqrt((-10)^2 - 4*1*9)/(2*1)
this becomes:
(10 +- sqrt(100-36))/2
this becomes:
(10 +- sqrt(64))/2
this becomes:
(10 +- 8)/2
this becomes:
18/2 = 9
or:
2/2 = 1
you get:
x = 9 or x = 1
substitute in original equation to see if these values are good.
original equation is:
x^2 - 10x = -9
when x = 9, this becomes:
81 - 90 = -9 which becomes -9 = -9 which is true.
when x = 1, this becomes:
1 - 10 = -9 = -9 which is also true.
the values are confirmed to be good.
your solutions are:
x = 9 and x = 1
these are the real roots of this equation which means that the graph of the equation crosses the x-axis at these points.
a graph of your equation looks like this:
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