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dem82 [27]
3 years ago
11

Solve x^2=2x+3 by factoring

Mathematics
1 answer:
solong [7]3 years ago
4 0

The solution is x = 1 and x = -3

<em><u>Solution:</u></em>

Given that we have to solve the given equation by factoring

Given equation is:

x^2=2x + 3\\\\x^2 - 2x - 3 = 0

\text{Consider the form } x^2+bx+c

Find a pair of integers whose product is c and and whose sum is b

\text{Compare } x^2-2x-3 = 0 \text{ with } x^2+bx +c\\\\\text{We get } b = -2 \text{ and } c = -3

Now find, a pair of integers whose sum is -2 and product is -3

The integers that satisfies this condition is -1 and 3

When we add - 1 and 3 we get 2

When multiply -1 and 3 we get -3

Thus the pair of integers are -1 and 3

Write the factored form using these integers.

(x-1)(x+3) = 0

The Zero Product Property states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0

Set the factors equal to 0

x - 1 = 0 \text{ and } x + 3 = 0

x = 1 and x = -3

Thus the solution is x = 1 and x = -3

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