 # Solving Equations. A quadratic equation is an equation equivalent to one of the form Where a, b, and c are real numbers and a  0 To solve a quadratic.

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Solving Equations

A quadratic equation is an equation equivalent to one of the form Where a, b, and c are real numbers and a  0 To solve a quadratic equation we get it in the form above and see if it will factor. Get form above by subtracting 5x and adding 6 to both sides to get 0 on right side. -5x + 6 Factor. Use the Zero property of multiplication and set each factor = 0 and solve. So if we have an equation in x and the highest power is 2, it is quadratic.

What if in standard form, c = 0? We could factor by pulling an x out of each term. Factor out the common x Use the Null Factor law and set each factor = 0 and solve. If you put either of these values in for x in the original equation you can see it makes a true statement.

In this form we could have the case where b = 0. Remember standard form for a quadratic equation is: When this is the case, we get the x 2 alone and then square root both sides. Get x 2 alone by adding 6 to both sides and then dividing both sides by 2 + 6 22 Now take the square root of both sides remembering that you must consider both the positive and negative root.  Let's check: Now take the square root of both sides remembering that you must consider both the positive and negative root.

In this form we could have the case where b = 0. Another example: When this is the case, we get the x 2 alone and then square root both sides. Get x 2 alone by adding 18 to both sides and then dividing both sides by 3 + 18 33 Now take the square root of both sides remembering that you must consider both the positive and negative root.  Let's check: Now take the square root of both sides remembering that you must consider both the positive and negative root.

To simplify radicals: look for a square factor or a pair of factors

= Square Root of a product You can break a square root into two square roots over a multiplication sign.

A pair square number under the Radical The square of the square number can be calculated to simplify the radicand

1 1 = 1 2 2 = 4 3 3 = 9 4 4 = 16 5 5 = 25 6 6 = 36 49, 64, 81, 100, 121, 144, 169, 196, 225, 256 You should know your square numbers

= A pair of numbers under the Radical The square and square root undo each other = 2 = original number

= = = = LEAVE IN RADICAL FORM You have to make sure that your final answer is simplified all the way =

= = = = LEAVE IN RADICAL FORM You have to make sure that your final answer is simplified all the way =