SOLUTION: Use the quadratic formula to solve the equation. If the equation has no real number solutions, so state. x^2 + 7x + 2 = 0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Use the quadratic formula to solve the equation. If the equation has no real number solutions, so state. x^2 + 7x + 2 = 0      Log On


   

Question 248250: Use the quadratic formula to solve the equation. If the equation has no real number solutions, so state. x^2 + 7x + 2 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B7%2Ax%2B2=0 ( notice a=1, b=7, and c=2)





x+=+%28-7+%2B-+sqrt%28+%287%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 Plug in a=1, b=7, and c=2




x+=+%28-7+%2B-+sqrt%28+49-4%2A1%2A2+%29%29%2F%282%2A1%29 Square 7 to get 49




x+=+%28-7+%2B-+sqrt%28+49%2B-8+%29%29%2F%282%2A1%29 Multiply -4%2A2%2A1 to get -8




x+=+%28-7+%2B-+sqrt%28+41+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-7+%2B-+sqrt%2841%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+=+%28-7+%2B-+sqrt%2841%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-7+%2B+sqrt%2841%29%29%2F2 or x+=+%28-7+-+sqrt%2841%29%29%2F2



Now break up the fraction



x=-7%2F2%2Bsqrt%2841%29%2F2 or x=-7%2F2-sqrt%2841%29%2F2



Simplify



x=-7%2F2%2Bsqrt%2841%29%2F2 or x=-7%2F2-sqrt%2841%29%2F2



So the solutions are:

x=-7%2F2%2Bsqrt%2841%29%2F2 or x=-7%2F2-sqrt%2841%29%2F2