Solve the following equation by grouping. x^2+10x+21=0
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To solve the equation by grouping, we need to break up the middle term in the quadratic equation.
We notice that the coefficient of the middle term, 10, can be factored as 7 + 3.
So, we rewrite the equation as:
x^2 + 7x + 3x + 21 = 0
Now, we group the terms in pairs:
(x^2 + 7x) + (3x + 21) = 0
Next, we factor out the greatest common factor from each pair:
x(x + 7) + 3(x + 7) = 0
Notice that (x + 7) is common to both terms. So we can factor it out:
(x + 7)(x + 3) = 0
Now we use the Zero Product Property:
x + 7 = 0 or x + 3 = 0
Solving each equation separately, we get:
x = -7 or x = -3
Therefore, the solution to the equation x^2 + 10x + 21 = 0 is x = -7 or x = -3.