Use inspection to solve the equation x^2 = 81, then select the complete solution set below, If there are no real solutions, select '' There are no real solutions.''
To solve the equation x^2 = 81 by inspection, we can determine the value of x that satisfies the given equation.
By inspection, we can see that the square root of 81 is 9 because 9 * 9 = 81. Therefore, x can be either positive or negative 9.
Hence, the complete solution set for the equation x^2 = 81 is: {-9, 9}.
Use inspection to solve the equation x^2 = 36/169, then select the correct solution set below. If there are no real solutions, select ''There are no real solutions.''
To solve the equation x^2 = 36/169 by inspection, we can determine the value of x that satisfies the given equation.
By inspection, we can see that the square root of 36/169 is 6/13 because (6/13) * (6/13) = 36/169. Therefore, x can be either positive or negative 6/13.
Hence, the correct solution set for the equation x^2 = 36/169 is: {-6/13, 6/13}.
Solve the following quadratic using square roots: (x - 18)^2 = 196
To solve the quadratic equation (x - 18)^2 = 196 using square roots, we can isolate the squared term on one side of the equation and then take the square root of both sides.
Taking the square root of both sides, we have:
√((x - 18)^2) = √(196)
Simplifying the square root of the squared term, we have:
|x - 18| = √(196)
Now, we can remove the absolute value and split the equation into two cases:
Case 1: x - 18 = √(196)
Simplifying this case, we have:
x - 18 = 14
Solving for x, we get:
x = 14 + 18
x = 32
Case 2: x - 18 = -√(196)
Simplifying this case, we have:
x - 18 = -14
Solving for x, we get:
x = -14 + 18
x = 4
Hence, the solution set for the quadratic equation (x - 18)^2 = 196 is {4, 32}.
Solve the following quadratic using square roots: (x - 18)^2 = 196.
A. {-4,-32}
B. {214,-178}
C. {21,5}
D. {32,4}
To solve the quadratic equation (x - 18)^2 = 196 using square roots, we can isolate the squared term on one side of the equation and then take the square root of both sides.
Taking the square root of both sides, we have:
√((x - 18)^2) = √(196)
Simplifying the square root of the squared term, we have:
|x - 18| = √(196)
Now, we can remove the absolute value and split the equation into two cases:
Case 1: x - 18 = √(196)
Simplifying this case, we have:
x - 18 = 14
Solving for x, we get:
x = 14 + 18
x = 32
Case 2: x - 18 = -√(196)
Simplifying this case, we have:
x - 18 = -14
Solving for x, we get:
x = -14 + 18
x = 4
Hence, the solution set for the quadratic equation (x - 18)^2 = 196 is {4, 32}.
Therefore, the correct answer is:
D. {32,4}
Solve the following quadratic using square roots: (x+6)^2/2 = 8.
A. {-2,-10}
B. {-117,-6.83}
C. {10,-22}
D. {-0.34,-11.66}
To solve the quadratic equation (x+6)^2/2 = 8 using square roots, we can first multiply both sides by 2 to eliminate the fraction:
(x+6)^2 = 16
Next, we can take the square root of both sides:
√((x+6)^2) = √16
Now, we can simplify:
|x+6| = 4
We can now remove the absolute value and split the equation into two cases:
Case 1: x+6 = 4
Simplifying this case, we have:
x = 4 - 6
x = -2
Case 2: x+6 = -4
Simplifying this case, we have:
x = -4 - 6
x = -10
Hence, the solution set for the quadratic equation (x+6)^2/2 = 8 is {-2, -10}.
Therefore, the correct answer is:
A. {-2,-10}