SOLUTION: SOLVE x^2-10x+29=0 ANSWER CHOICES A. -5 +4i, -5-4i B. -5 +2i, -5-2i C. 5 +4i, 5-4i D. 5 +2i, 5-2i

Algebra ->  Rational-functions -> SOLUTION: SOLVE x^2-10x+29=0 ANSWER CHOICES A. -5 +4i, -5-4i B. -5 +2i, -5-2i C. 5 +4i, 5-4i D. 5 +2i, 5-2i      Log On


   

Question 595870: SOLVE
x^2-10x+29=0
ANSWER CHOICES
A. -5 +4i, -5-4i
B. -5 +2i, -5-2i
C. 5 +4i, 5-4i
D. 5 +2i, 5-2i
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-10x%2B29=0 Start with the given equation.


Notice that the quadratic x%5E2-10x%2B29 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-10, and C=29


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-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%281%29%2829%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-10, and C=29


x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%281%29%2829%29+%29%29%2F%282%281%29%29 Negate -10 to get 10.


x+=+%2810+%2B-+sqrt%28+100-4%281%29%2829%29+%29%29%2F%282%281%29%29 Square -10 to get 100.


x+=+%2810+%2B-+sqrt%28+100-116+%29%29%2F%282%281%29%29 Multiply 4%281%29%2829%29 to get 116


x+=+%2810+%2B-+sqrt%28+-16+%29%29%2F%282%281%29%29 Subtract 116 from 100 to get -16


x+=+%2810+%2B-+sqrt%28+-16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2810+%2B-+4%2Ai%29%2F%282%29 Take the square root of -16 to get 4%2Ai.


x+=+%2810+%2B+4%2Ai%29%2F%282%29 or x+=+%2810+-+4%2Ai%29%2F%282%29 Break up the expression.


x+=+%2810%29%2F%282%29+%2B+%284%2Ai%29%2F%282%29 or x+=++%2810%29%2F%282%29+-+%284%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+5%2B2%2Ai or x+=++5-2%2Ai Reduce.


So the solutions are x+=+5%2B2%2Ai or x+=+5-2%2Ai