Any other quadratic equation is best solved by using the Quadratic Formula. If the equation fits the form ax 2 = k or a( x − h) 2 = k, it can easily be solved by using the Square Root Property. If the quadratic factors easily, this method is very quick.
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if b 2 − 4 ac = 0, the equation has 1 real solution.If b 2 − 4 ac > 0, the equation has 2 real solutions.For a quadratic equation of the form ax 2 + bx + c = 0,.Remember the helpful saying: The angry bee is deciding whether or not to go into the house where the other bees are square dancing and losing to 4 aces at the party that is all over at 2 am. Using the Discriminant, b 2 − 4 ac, to Determine the Number and Type of Solutions of a Quadratic Equation First, Memorize the Quadratic Formula: The quadratic equation ax2 + b x + c 0 has solution a b b ac x 2 ± 2 4.Then substitute in the values of a, b, c. Write the quadratic equation in standard form, ax 2 + bx + c = 0. Learn how to solve quadratic equations using different methods, such as factoring, completing the square, and the quadratic formula.How to solve a quadratic equation using the Quadratic Formula.We start with the standard form of a quadratic equation and solve it for x by completing the square. Now we will go through the steps of completing the square using the general form of a quadratic equation to solve a quadratic equation for x. We have already seen how to solve a formula for a specific variable ‘in general’, so that we would do the algebraic steps only once, and then use the new formula to find the value of the specific variable. In this section we will derive and use a formula to find the solution of a quadratic equation. Mathematicians look for patterns when they do things over and over in order to make their work easier. By the end of the exercise set, you may have been wondering ‘isn’t there an easier way to do this?’ The answer is ‘yes’.
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When we solved quadratic equations in the last section by completing the square, we took the same steps every time. Solve Quadratic Equations Using the Quadratic Formula