SOLUTION: Can you help me use the zero property or factoring to find the solution of (x+2)(2x+7)=-15 ?

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Question 449355: Can you help me use the zero property or factoring to find the solution of (x+2)(2x+7)=-15 ?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Quadratic Equation in Standard Form
ax%5E2%2Bbx%2Bc=0
where a does not equal 0.
Zero Factor Property
If a product ab+=+0, then a+=+0 or b+=+0.
0 is our magic number because the only way a product can become 0 is if at least one of its factors is 0
you need:
use the zero property or factoring to find the solution of
%28x%2B2%29%282x%2B7%29=-15+....first set equation = to 0
%28x%2B2%29%282x%2B7%29%2B15=0+multiply

2x%5E2%2B4x%2B7x%2B14%2B15=0+

2x%5E2%2B11x%2B29=0+.....since 2x%5E2%2B11x%2B29=0+ cannot be factored,. ... you cannot find the solution of %28x%2B2%29%282x%2B7%29=-15+ by using the zero property or factoring
only way is to use quadratic formula
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 2%2Ax%5E2%2B11%2Ax%2B29=0 ( notice a=2, b=11, and c=29)





x+=+%28-11+%2B-+sqrt%28+%2811%29%5E2-4%2A2%2A29+%29%29%2F%282%2A2%29 Plug in a=2, b=11, and c=29




x+=+%28-11+%2B-+sqrt%28+121-4%2A2%2A29+%29%29%2F%282%2A2%29 Square 11 to get 121




x+=+%28-11+%2B-+sqrt%28+121%2B-232+%29%29%2F%282%2A2%29 Multiply -4%2A29%2A2 to get -232




x+=+%28-11+%2B-+sqrt%28+-111+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-11+%2B-+i%2Asqrt%28111%29%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-11+%2B-+i%2Asqrt%28111%29%29%2F%284%29 Multiply 2 and 2 to get 4




After simplifying, the quadratic has roots of


x=-11%2F4%2Bsqrt%28111%29%2F4%2Ai or x=-11%2F4-sqrt%28111%29%2F4%2Ai




as you can see, there is NO real solutions, only imaginary solutions