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: