Solve by using the quadratic formula
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To solve a quadratic equation using the quadratic formula, you will need to know the coefficients of the quadratic terms, which are usually denoted by the variables a, b, and c.
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
To use this formula, you need to substitute the values of a, b, and c into the equation. Make sure to pay attention to the sign before each term.
The discriminant, which is the value inside the square root (b^2 - 4ac), will help determine the nature of the solutions:
1. If the discriminant is positive (√(b^2 - 4ac) > 0), then there are two distinct real solutions.
2. If the discriminant is zero (√(b^2 - 4ac) = 0), then there is one real solution (usually referred to as a double root or repeated root).
3. If the discriminant is negative (√(b^2 - 4ac) < 0), then there are no real solutions, and the equation has complex solutions.
Once you have calculated the values of x using the quadratic formula, you can simplify the solutions if needed.
Remember to double-check your calculations, as errors can sometimes occur when performing complex calculations.