Explain how to solve a quadratic equation using the quadratic formula.
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first identify your a,b and c.don't forget the signs.then simply substitute in the formula which is;
x=-b plus or minus square root of b^2 - 4ac,everything over 2a.btw the root is for everthing execpt the -b and 2a
To solve a quadratic equation using the quadratic formula, which is a formula that gives the solutions to any quadratic equation, follow these steps:
1. Write down the quadratic equation in the form of ax^2 + bx + c = 0. Here, 'a', 'b', and 'c' are coefficients. For example, let's take the equation 2x^2 - 5x + 3 = 0.
2. Identify the values of 'a', 'b', and 'c' from the equation. In our example equation, 'a' is 2, 'b' is -5, and 'c' is 3.
3. Substitute the values of 'a', 'b', and 'c' into the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a). This formula gives two possible solutions for 'x', denoted by the ± symbol.
4. Calculate the discriminant, which is the value under the square root in the quadratic formula, given by b^2 - 4ac. In our example, the discriminant is (-5)^2 - 4(2)(3) = 25 - 24 = 1.
5. Calculate the square root of the discriminant. In our example, √1 = 1.
6. Substitute the values of 'b', the square root of the discriminant, and 'a' into the quadratic formula, and simplify the expression. In our example, x = (-(-5) ± 1) / (2(2)) = (5 ± 1) / 4.
7. Calculate the two possible solutions by simplifying the expression obtained from step 6. The two solutions in our example are x = (5 + 1) / 4 = 6 / 4 = 3/2 and x = (5 - 1) / 4 = 4 / 4 = 1.
So, the two solutions to the quadratic equation 2x^2 - 5x + 3 = 0 are x = 3/2 and x = 1.