4x²-25=0
Hint: factor it using difference of squares method
To solve the equation 4x² - 25 = 0, you can use the method called factoring or the quadratic formula. Let's explain both methods:
Method 1: Factoring
Step 1: Write the equation in the form of (ax + b)(cx + d) = 0
4x² - 25 = (2x + 5)(2x - 5) = 0
Step 2: Set each factor equal to zero and solve for x:
2x + 5 = 0 or 2x - 5 = 0
Step 3: Solve for x in each equation:
2x + 5 = 0 2x - 5 = 0
2x = -5 2x = 5
x = -5/2 x = 5/2
So the solutions to the equation 4x² - 25 = 0 are x = -5/2 and x = 5/2.
Method 2: Quadratic Formula
The quadratic formula can be used to solve any quadratic equation in the form ax² + bx + c = 0. In this case, the equation 4x² - 25 = 0 can be rewritten as 4x² + 0x - 25 = 0. Comparing this to the general form ax² + bx + c = 0, we have a = 4, b = 0, and c = -25.
The quadratic formula is: x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values from our equation:
x = (-(0) ± √((0)² - 4(4)(-25))) / (2(4))
= ± √(0 + 400) / 8
= ± √(400) / 8
= ± 20 / 8
= ± 5/2
So the solutions to the equation 4x² - 25 = 0 are x = -5/2 and x = 5/2.