SOLUTION: Solve the equation. Write the solutions in the form a+bi. x^2+10x+30=0

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Question 188659This question is from textbook saxon algebra 2
: Solve the equation. Write the solutions in the form a+bi.
x^2+10x+30=0
 This question is from textbook saxon algebra 2

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B10x%2B30=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=10, and c=30


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-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%281%29%2830%29+%29%29%2F%282%281%29%29 Plug in a=1, b=10, and c=30


x+=+%28-10+%2B-+sqrt%28+100-4%281%29%2830%29+%29%29%2F%282%281%29%29 Square 10 to get 100.


x+=+%28-10+%2B-+sqrt%28+100-120+%29%29%2F%282%281%29%29 Multiply 4%281%29%2830%29 to get 120


x+=+%28-10+%2B-+sqrt%28+-20+%29%29%2F%282%281%29%29 Subtract 120 from 100 to get -20


x+=+%28-10+%2B-+sqrt%28+-20+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-10+%2B-+2i%2Asqrt%285%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-10%29%2F%282%29+%2B-+%282i%2Asqrt%285%29%29%2F%282%29 Break up the fraction.


x+=+-5+%2B-+sqrt%285%29%2Ai Reduce.


x+=+-5%2Bsqrt%285%29%2Ai or x+=+-5-sqrt%285%29%2Ai Break up the expression.


So the answers are x+=+-5%2Bsqrt%285%29%2Ai or x+=+-5-sqrt%285%29%2Ai



So the solutions are in the form a%2Bbi where a=-5 (for both solutions), b=sqrt%285%29 for the first solution, and b=-sqrt%285%29 for the second solution.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation. Write the solutions in the form a+bi.
x^2+10x+30=0
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Quadratic formula:
x = [-10 +- sqrt(100 - 4*1*30)]/2
x = [-10 +- sqrt(-20)]/2
x = [-10 +- 2isqrt(5)]/2
x = [-5 +- isqrt(5)]
x = (-5 + isqrt(5)) or x = (-5 - isqrt(5))
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Cheers,
Stan H.