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Factor the equation (xt3)^2 +(x+3) -2 =0

Factor the equation (xt3)^2 +(x+3) -2 =0-example-1
User Nextstep
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1 Answer

6 votes

x^2 makes the graph looks like a U

if it where just x the graph would look like a straight line or /

"factor" means the graph goes thru the x axis at -5 & -2 when y is 0

"factor" means the graph goes thru the x axis at (-5,0) & (-2,0)

Answer:

x = -5

x = -2

Explanation:

combine like terms:

(x+3)^2 + (x+3) - 2 = 0

x^2 + 6x + 9 + x + 3 - 2 = 0

x^2 + 7x + 10 = 0

We can now factor the quadratic expression by finding two numbers that multiply to give us `10` and add up to give us `7`. These numbers are `2` and `5`. Therefore, we can write:

x^2 + 7x + 10 = (x+2)(x+5)

Thus, the factored form of the given equation is:

(x+2)(x+5) = 0

Therefore, the solutions to the equation are:

x = -2 or x = -5

claudeAI

User Fightlight
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