SOLUTION: 2. Solve the equation by using the quadratic formula. Use √( ) and ± , if you want. a. Write irrational numbers in simplest radical form. b. Explain each step as you

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 2. Solve the equation by using the quadratic formula. Use √( ) and ± , if you want. a. Write irrational numbers in simplest radical form. b. Explain each step as you      Log On


   

Question 457407: 2. Solve the equation by using the quadratic formula. Use √( ) and ± , if you want.
a. Write irrational numbers in simplest radical form.
b. Explain each step as you go.
X^2 + 4x – 8 = 0
Answer by MathLover1(20850) 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%2B4%2Ax-8=0 ( notice a=1, b=4, and c=-8)





x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29 Plug in a=1, b=4, and c=-8




x+=+%28-4+%2B-+sqrt%28+16-4%2A1%2A-8+%29%29%2F%282%2A1%29 Square 4 to get 16




x+=+%28-4+%2B-+sqrt%28+16%2B32+%29%29%2F%282%2A1%29 Multiply -4%2A-8%2A1 to get 32




x+=+%28-4+%2B-+sqrt%28+48+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-4+%2B-+4%2Asqrt%283%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+=+%28-4+%2B-+4%2Asqrt%283%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-4+%2B+4%2Asqrt%283%29%29%2F2 or x+=+%28-4+-+4%2Asqrt%283%29%29%2F2



Now break up the fraction



x=-4%2F2%2B4%2Asqrt%283%29%2F2 or x=-4%2F2-4%2Asqrt%283%29%2F2



Simplify



x=-2%2B2%2Asqrt%283%29 or x=-2-2%2Asqrt%283%29



So the solutions are:

x=-2%2B2%2Asqrt%283%29 or x=-2-2%2Asqrt%283%29