Can you please help me with the steps to working this equation?
x + 8/x = -9
First, LCD = x
x(x)+ x(8/x) = x(-9)
x^2+8 = -9x
Now add 9x both
x^2+9x+8 = 0
Factor: (x+8)(x+1) = 0
x+ 8 = 0. x+1= 0
x+8-8 = 0-8. x+1-1 = 0-1
x= -8. x= -1
x= -8, -1
Another way :
x + 8 / x = - 9 Multiply both sides by x
x ^ 2 + 8 = - 9 x Add 9 x to both sides
x ^ 2 + 8 + 9 x = - 9 x + 9 x
x ^ 2 + 9 x + 8 = 0
In google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
x ^ 2 + 9 x + 8 = 0
and click option: solve it
You will see solution step-by step
Of course! I can help you work through the equation step by step.
Step 1: Start by multiplying both sides of the equation by x to eliminate the denominator:
x(x + 8/x) = -9x
Step 2: Simplify the left side of the equation by distributing x to both terms inside the parentheses:
x² + 8 = -9x
Step 3: Rearrange the equation by moving all terms to one side, usually the left side, to set the equation equal to zero:
x² + 9x + 8 = 0
Step 4: Now we have a quadratic equation in standard form. We can factor it or use the quadratic formula to solve for x. Let's try factoring first:
The factors of 8 are:
1 and 8,
2 and 4.
We are looking for factors that add up to 9 (the coefficient of x). Upon inspection, we see that 1 and 8 do not add up to 9, but 1 and 8 do.
So rewrite the equation using the appropriate factors:
(x + 1)(x + 8) = 0
Step 5: Set each factor equal to zero and solve for x:
x + 1 = 0 or x + 8 = 0
Solving each equation separately:
For x + 1 = 0, subtract 1 from both sides:
x = -1
For x + 8 = 0, subtract 8 from both sides:
x = -8
Step 6: Check your solutions by substituting them back into the original equation:
Substitute x = -1:
-1 + 8/(-1) = -9
Simplifying the equation:
-1 - 8 = -9
-9 = -9
Substitute x = -8:
-8 + 8/(-8) = -9
Simplifying the equation:
-8 - 1 = -9
-9 = -9
Step 7: Both solutions, x = -1 and x = -8, satisfy the original equation, so these are the solutions to the equation x + 8/x = -9.
I hope this explanation helps! Let me know if you have any further questions.