Solve 4x^2-1 = 0
Solve ax² + bx + c = 0 using the quadratic formula with discriminant analysis.
4x2-1=0
Solve by isolating x² and taking the square root of both sides:
Move 1 to the other side:
4x2 = 1
Divide both sides by 4 to get x² alone:
x2 = 14
Since x² = k has two solutions, x = +√k and x = −√k:
x = ±√14
x = ±12
x = ±12
How to solve 4x^2-1 = 0
To solve 4x^2-1 = 0, we can try factoring, use the quadratic formula, or complete the square. The solution is x = ±1/2.
This is a second-degree quadratic equation — the highest power of the variable is 2. Quadratic equations can have two real roots, one repeated root, or two complex roots.
Frequently asked questions
What is the answer to 4x^2-1 = 0?
The answer is x = ±1/2.
What method is used?
factoring when possible, or the quadratic formula x = (−b ± √(b²−4ac)) / 2a. The discriminant b²−4ac determines the number and type of solutions.
How do I verify this?
Substituting the solution(s) back into 4x^2-1 = 0 confirms both sides are equal.