Solve the problem by factoring: x^2 + 10x + 13 = 4 show how you solved it

Solve the quadratic equation by factoring:

x² + 10x + 13 = 4

Subtract  4  from both sides:

x² + 10x + 13 – 4 = 4 – 4

x² + 10x + 9 = 0

Now, look for two numbers so their sum is  10, and their product is  9. You can search within the set of the divisors of  9, for instance:

D(9) = {1, 3, 9}

Taking the numbers  1  and  9, you find that

•  1 + 9 = 10;

•  1 · 9 = 9.

So, in the equation, rewrite conveniently  10x  as  9x + x, then it becomes

x² + 9x + x + 9 = 0

Factor the equation above by grouping. Take out the common factor  x  from the first two terms at the left-hand side:

x · (x + 9) + x + 9 = 0

x · (x + 9) + 1 · (x + 9) = 0

Now, take out the common factor  (x + 9):

(x + 9) · (x + 1) = 0

If a product equals zero, the one of the factors must be zero:

x + 9 = 0   or   x + 1 = 0

x = – 9   or   x = – 1     <———    those are the solutions.

Solution set:   S = {– 9,  – 1}.

I hope this helps. =)

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