Solve the quadratic equations. Find the value/values of x (use extracting square roots). Show your solution. 1. x² - 49 = 0 2. 9x² - 25 = 0 3. 4x² + 1 = 5

Let's solve each quadratic equation using the method of extracting square roots.

Equation: x 2 − 49 = 0
Step-by-step solution:

Start by moving 49 to the other side of the equation: x 2 = 49

Take the square root of both sides: x = ± 49 ​

Simplify the square root: x = ± 7

Therefore, the solutions are x = 7 and x = − 7 .



Equation: 9 x 2 − 25 = 0
Step-by-step solution:

Move 25 to the other side: 9 x 2 = 25

Divide each side by 9: x 2 = 9 25 ​

Take the square root of both sides: x = ± 9 25 ​ ​

Simplify the square root: x = ± 3 5 ​

So, the solutions are x = 3 5 ​ and x = − 3 5 ​ .



Equation: 4 x 2 + 1 = 5
Step-by-step solution:

Subtract 1 from both sides: 4 x 2 = 4

Divide each side by 4: x 2 = 1

Take the square root of both sides: x = ± 1 ​

Simplify the square root: x = ± 1

Thus, the solutions are x = 1 and x = − 1 .




In summary, by extracting square roots, we found the following solutions for each equation:

For x 2 − 49 = 0 , the solutions are x = 7 and x = − 7 .
For 9 x 2 − 25 = 0 , the solutions are x = 3 5 ​ and x = − 3 5 ​ .
For 4 x 2 + 1 = 5 , the solutions are x = 1 and x = − 1 .

Answered by LucasMatthewHarris | 2025-07-21