Answer:
x=-4,x= -14
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x2+18x+81=25
Step 2: Subtract 25 from both sides.
x2+18x+81−25=25−25
x2+18x+56=0
Step 3: Factor left side of equation.
(x+4)(x+14)=0
Step 4: Set factors equal to 0.
x+4=0 or x+14=0
x=−4 or x=−14
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Explanation:
Apply the square root to both sides
(x+9)^2 = 25 leads to x+9 = 5 or x+9 = -5
This is because (-5)^2 = 25 and (5)^2 = 25. This is the plus/minus you often see with quadratics.
Solve x+9 = 5 to get x = -4. We subtract 9 from both sides to get this.
Solve x+9 = -5 to get x = -14
That's why the two answers are x = -4 and x = -14.
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To check our answers, we plug those x values into the original equation and simplify. We should get the same thing on both sides
(x+9)^2 = 25
(-4+9)^2 = 25 ... replace x with -4
(5)^2 = 25
25 = 25 ... So x = -4 has been confirmed
and,
(x+9)^2 = 25
(-14+9)^2 = 25 ... replace x with -14
(-5)^2 = 25
25 = 25 ... and x = -14 has been confirmed
