Solve the following quadratic equation using square roots: (x−18)^2=196.
{32,4} left brace 32 comma 4 right brace {214,−178} left brace 214 comma negative 178 right brace {21,5} left brace 21 comma 5 right brace {−4,−32} left brace negative 4 comma negative 32 right brace
To solve the equation using square roots, we can take the square root of both sides of the equation:
√((x−18)^2) = √196
(x−18) = ±√196
(x−18) = ±14
To find the solutions, we can solve the two equations separately:
1) (x−18) = 14
Adding 18 to both sides, we get:
x = 14 + 18
x = 32
2) (x−18) = -14
Adding 18 to both sides, we get:
x = -14 + 18
x = 4
Therefore, the solutions to the equation (x−18)^2=196 are x = 32 and x = 4.
To solve the quadratic equation (x−18)² = 196 using square roots, we can follow these steps:
Step 1: Take the square root of both sides of the equation.
√((x−18)²) = √196
Step 2: Simplify the equation.
x−18 = ±√196
Step 3: Simplify the square root of 196.
x−18 = ±14
Step 4: Solve for x.
Option 1: x−18 = 14
Adding 18 to both sides: x = 14 + 18 = 32
Option 2: x−18 = -14
Adding 18 to both sides: x = -14 + 18 = 4
Therefore, the solutions to the quadratic equation (x−18)² = 196 using square roots are x = 32 and x = 4.
To solve the quadratic equation (x−18)² = 196 using square roots, follow these steps:
Step 1: Rewrite the equation in standard form.
(x−18)² = 196
Step 2: Take the square root of both sides of the equation.
√[(x−18)²] = ±√196
Step 3: Simplify the square root on the left side.
|x−18| = ±14
Step 4: Solve for x by considering both positive and negative values.
x−18 = 14 or x−18 = -14
Step 5: Solve each equation separately.
For x−18 = 14:
Add 18 to both sides: x = 18 + 14 = 32
For x−18 = -14:
Add 18 to both sides: x = 18 - 14 = 4
Therefore, the solutions for the quadratic equation (x−18)² = 196 using square roots are x = 32 and x = 4.