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What are the solutions of the quadratic equation (x+3)^2=49?

a. x=2 and
√(-10)
b. x=-2 and x= -16
c. x = 40 and x = –58
d. x = 4 and x = –10

User Eunhee
by
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2 Answers

7 votes


\huge\text{Hey there!}



\mathsf{(x + 3)^2 = 49}\\\mathsf{(x + 3)(x + 3) = 49}\\\mathsf{x(x) + x(3) + 3(x) + 3(3) = 49}\\\mathsf{x(x) + 3(x) + 3(x) + 3(3) = 49}\\\mathsf{x^2 + 3x + 3x + 9 = 49}\\\mathsf{x^2 + 6x + 9 = 49}\\\\\large\text{SUBTRACT 49 to BOTH SIDES}\\\mathsf{x^2 + 6x + 9 - 49 = 49 - 49}\\\large\text{SIMPLIFY IT!}\\\\\large\text{FACTOR the LEFT SIDE}\\\mathsf{(x - 4)(x + 10) = 0}\\\\\large\text{SET the FACTORS TO EQUAL 0}\\\mathsf{x - 4 = 0 \ or\ x + 10 = 0}\\\large\text{SIMPLIFY IT!}\\\\\mathsf{x = 4\ or \ x = -10}



\large\textsf{Therefore, your answer is: \huge\boxed{\mathsf{Option\ D. x = 4\ or\ x = -10}}}\huge\checkmark



\huge\text{Good luck on your assignment \& enjoy your day!}


~
\frak{Amphitrite1040:)}

User Denoteone
by
4.9k points
4 votes

Answer:

d. x = 4 and x = –10

Explanation:

(x+3)^2=49

Take the square root of each side

sqrt((x+3)^2)=±sqrt(49)

x+3 = ±7

Separate into 2 equations

x+3 = 7 x+3 = -7

Subtract 3 from each side

x+3-3=7-3 x+3-3 = -7-3

x =4 x =-10

User BamaPookie
by
4.5k points