SOLUTION: can you describe how to do x^2 - 9x - 22 = 0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: can you describe how to do x^2 - 9x - 22 = 0       Log On


   

Question 569954: can you describe how to do x^2 - 9x - 22 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-9x-22=0 Start with the given equation.


Notice that the quadratic x%5E2-9x-22 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-9, and C=-22


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2-4%281%29%28-22%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-9, and C=-22


x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%281%29%28-22%29+%29%29%2F%282%281%29%29 Negate -9 to get 9.


x+=+%289+%2B-+sqrt%28+81-4%281%29%28-22%29+%29%29%2F%282%281%29%29 Square -9 to get 81.


x+=+%289+%2B-+sqrt%28+81--88+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-22%29 to get -88


x+=+%289+%2B-+sqrt%28+81%2B88+%29%29%2F%282%281%29%29 Rewrite sqrt%2881--88%29 as sqrt%2881%2B88%29


x+=+%289+%2B-+sqrt%28+169+%29%29%2F%282%281%29%29 Add 81 to 88 to get 169


x+=+%289+%2B-+sqrt%28+169+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%289+%2B-+13%29%2F%282%29 Take the square root of 169 to get 13.


x+=+%289+%2B+13%29%2F%282%29 or x+=+%289+-+13%29%2F%282%29 Break up the expression.


x+=+%2822%29%2F%282%29 or x+=++%28-4%29%2F%282%29 Combine like terms.


x+=+11 or x+=+-2 Simplify.


So the solutions are x+=+11 or x+=+-2