Solve the following quadratic equation using square roots: (x−18)2=196 .(1 point) Responses {−4,−32} left brace negative 4 comma negative 32 right brace {214,−178} left brace 214 comma negative 178 right brace {32,4} left brace 32 comma 4 right brace {21,5}
To solve the equation (x−18)² = 196, we can take the square root of both sides:
√((x−18)²) = √196
This simplifies to:
x−18 = ±14
Now, we can add 18 to both sides to isolate x:
x = 18 ± 14
So the solutions to the quadratic equation are:
x = 18 + 14 = 32
x = 18 - 14 = 4
Therefore, the correct answer is {32, 4}.
To solve the quadratic equation (x−18)^2=196 using square roots, we can take the square root of both sides of the equation:
√((x−18)^2) = √196
Simplifying the equation gives:
x−18 = ±√196
Now, we can solve for x by adding 18 to both sides of the equation:
x = 18 ± √196
Taking the square root of 196 gives us:
x = 18 ± 14
So, the two solutions to the equation are:
x = 18 + 14 = 32
x = 18 - 14 = 4
Therefore, the correct answer is {32, 4}.
To solve the quadratic equation (x − 18)^2 = 196 using square roots, you need to follow these steps:
Step 1: Rewrite the equation in its quadratic form.
(x − 18)^2 = 196
Step 2: Take the square root of both sides of the equation.
√(x − 18)^2 = ±√196
Step 3: Simplify both sides.
x − 18 = ±14
Step 4: Solve for x by adding 18 to both sides.
x = 18 ± 14
Step 5: Simplify the solutions.
x = 18 + 14 or x = 18 - 14
This gives us two solutions:
x = 32 or x = 4
So, the correct answer is {32, 4}.