SOLUTION: Solve using the quadratic formula. {{{x^2-10x=-23}}} Could someone please help me with this? I appreciate it.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve using the quadratic formula. {{{x^2-10x=-23}}} Could someone please help me with this? I appreciate it.      Log On


   

Question 295332: Solve using the quadratic formula.
x%5E2-10x=-23
Could someone please help me with this? I appreciate it.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-10x=-23 Start with the given equation


x%5E2-10x%2B23=0 Add 23 to both sides.


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-10%2Ax%2B23=0 ( notice a=1, b=-10, and c=23)





x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A23+%29%29%2F%282%2A1%29 Plug in a=1, b=-10, and c=23




x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A23+%29%29%2F%282%2A1%29 Negate -10 to get 10




x+=+%2810+%2B-+sqrt%28+100-4%2A1%2A23+%29%29%2F%282%2A1%29 Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because %28-10%29%5E2=-10%2A-10=100.)




x+=+%2810+%2B-+sqrt%28+100%2B-92+%29%29%2F%282%2A1%29 Multiply -4%2A23%2A1 to get -92




x+=+%2810+%2B-+sqrt%28+8+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2810+%2B-+2%2Asqrt%282%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2810+%2B-+2%2Asqrt%282%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%2810+%2B+2%2Asqrt%282%29%29%2F2 or x+=+%2810+-+2%2Asqrt%282%29%29%2F2



Now break up the fraction



x=%2B10%2F2%2B2%2Asqrt%282%29%2F2 or x=%2B10%2F2-2%2Asqrt%282%29%2F2



Simplify



x=5%2Bsqrt%282%29 or x=5-sqrt%282%29



So the solutions are:

x=5%2Bsqrt%282%29 or x=5-sqrt%282%29