The first step in solving a quadratic equation using the quadratic formula is to write the quadratic equation in standard form, ax2 + bx + c = 0.
Here's a breakdown of why and the subsequent steps:
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Standard Form: The quadratic formula is designed to work specifically when the equation is arranged in this standard format. This ensures that the coefficients a, b, and c are correctly identified.
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Identifying a, b, and c: Once in standard form, you must accurately identify the values of a, b, and c. These are the coefficients that will be substituted into the quadratic formula. a is the coefficient of the x2 term, b is the coefficient of the x term, and c is the constant term.
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Writing the Quadratic Formula: After identifying a, b, and c, write down the quadratic formula itself:
x = (-b ± √(b2 - 4ac)) / (2a)
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Substitution: The next step is to substitute the values of a, b, and c that you identified earlier into the quadratic formula.
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Simplification and Solution: Finally, simplify the expression obtained after substitution. This involves performing the arithmetic operations and solving for x. Remember, the "±" indicates that there are usually two solutions to a quadratic equation.
For example, consider the quadratic equation: 2x2 + 5x - 3 = 0
Here, a = 2, b = 5, and c = -3. These values would then be substituted into the quadratic formula.
