Solve Any Quadratic Equation With Ease Using The Quadratic Formula – Step By Step Guide And Example

quadratic formula

x = -b ± √(b² – 4ac)/2a

The quadratic formula is a general formula used to solve any quadratic equation, which can be written in the form of:

ax^2 + bx + c = 0, where a, b, and c are coefficients, and x is the variable.

The quadratic formula is:

x = (-b ± √(b^2 – 4ac)) / 2a

where ± indicates that there are two possible solutions, the positive and negative values.

To use the quadratic formula, we simply substitute the values of a, b, and c into the formula, compute the values of the positive and negative solutions, and verify that they satisfy the original equation.

For example, let’s solve the quadratic equation: 2x^2 + 5x – 3 = 0

In this case, a = 2, b = 5, and c = -3. Substituting these values into the quadratic formula, we get:

x = (-5 ± √(5^2 – 4(2)(-3))) / 2(2)
x = (-5 ± √(25 + 24)) / 4
x = (-5 ± √49) / 4

So, the two possible solutions are:

x = (-5 + 7) / 4 = 1/2
x = (-5 – 7) / 4 = -3

Therefore, the solutions of the quadratic equation 2x^2 + 5x – 3 = 0 are x = 1/2 and x = -3. We can verify that these solutions satisfy the equation by substituting them back into the original equation and observing that both sides of the equation are equal.

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