You can put this solution on YOUR website! Given to solve:
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You first need to get this into the standard quadratic form of:
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Do this by getting rid of the 6 on the right hand side. To make that happen, subtract 6 from both sides to get:
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On the left side the 15 and -6 combine to +9. And on the right side the 6 and -6 combine to zero. This changes the problem into:
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Note that this is in the standard quadratic form where "a" (which is the multiplier of the term) is equal to 1, b (which is the multiplier of the term) is -6, and c (the constant term) is +9.
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Quadratic equations are generally solved using one of three methods:
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a. factoring
b. completing the square
c. using the quadratic formula
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This problem can be solved by factoring. You can factor the left side into:
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Note that the two factors are the same. If you FOIL multiply these two factors you will get
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The factored equation will be true if either one of the two factors is equal to zero because a multiplication by zero on the left side makes the entire left side equal to zero which is equal to the right side.
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You can solve for the value or values of x that will make the factor equal to zero by setting each of the factors equal to zero and solving for x. This is as follows:
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add 3 to both sides to get rid of the -3 on the left side and this becomes:
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Since the other factor is the same, it also will go to zero if x = 3.
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So the solution to this problem is x = 3.
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Check by substitution 3 for x in the equation that you were given in the problem. Start with:
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Substitute 3 for x to get:
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Square the 3 and the equation becomes:
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Multiply the -6 times 3 to get -18 and the equation is then:
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Algebraically sum the left side. 9 + 15 = 24 and subtract 18 to get 6 on the left side. This equals the right side, so the answer checks. When x equals +3 the left side of the equation that you were originally given becomes equal to the right side.
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Hope this helps you to understand the problem. From lots of experience I was able to see that the left side would factor. However, not all quadratic equations can be factored. If you are unable to factor the left side, you can always use the quadratic formula to solve the quadratic equation. (We could have used the quadratic formula on this problem.) Using the quadratic formula is a whole different way of finding the answer and generally takes more work than factoring.
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