Can someone show me how to use the quadratic formula to solve this problem.This is for extra credit.I don't uderstand how to do this, so can someone point out the steps so I can be able to do the other five problem like this one. Thanks again for your help.
5/x+1=9-x
Is the left side 5/(x+1) or (5/x) + 1 ?
(5/x)+1=9-x
Certainly! I can explain how to solve the given problem using the quadratic formula.
Step 1: To begin, let's rewrite the equation in the correct format, which means getting rid of any fractions. Multiply both sides of the equation by (x + 1) to eliminate the fraction:
5/(x + 1) = 9 - x
5 = (9 - x)(x + 1)
Step 2: Expand the expression on the right side of the equation:
5 = 9(x + 1) - x(x + 1)
5 = 9x + 9 - x^2 - x
Step 3: Organize the equation into standard quadratic form, which is ax^2 + bx + c = 0. Rearrange the equation:
0 = -x^2 + 8x + 4
Step 4: Now, we can apply the quadratic formula to solve for x. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = -1, b = 8, and c = 4. Substituting these values into the formula, we get:
x = (-(8) ± √(8^2 - 4(-1)(4))) / (2(-1))
x = (-8 ± √(64 + 16)) / (-2)
x = (-8 ± √80) / (-2)
Step 5: Simplify the expression further:
x = (-8 ± √(16 × 5)) / (-2)
x = (-8 ± 4√5) / (-2)
Step 6: Finally, simplify the expression to get the two possible values for x:
x = (8 ± 4√5) / 2
x = 4 ± 2√5
So, the solution to the given equation is x = 4 + 2√5 or x = 4 - 2√5.
By following these steps, you can solve other problems similar to this one using the quadratic formula. Good luck with the remaining questions!