# Lesson Quadratic Equations You Cannot Factor

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This Lesson (Quadratic Equations You Cannot Factor) was created by by oberobic(2304)  : View Source, Show

Problem: We are given the following equation to solve for x:
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Solution: Start by getting the equation into standard form:
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In this case, subtract 2x from both sides.
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We can look for integer multiplicative factors of -9 that would leave us with -2 when added or subtracted.
9 = 1*9
9-1 = 8
-9+1 = -8
9 = 3*3
9-3 = 6
-9+3=-6
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So, we cannot simply factor this equation to solve it.
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At this point, looking at the graph is helpful.
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We can see there are two roots (zeroes) of x.
So, our choices are to complete the square or to use the quadratic equation.
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Completing the Square
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Isolate the 'c-term' on the right-hand side of the equation.
To do this, add 9 to both sides.

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Divide the x-term's coefficient ('b') in half.
-2/2 = -1
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Square this number and add to both sides of the equation
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Now define the squared term to be solved using the half-value of the x-term.
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Since the left-hand side is squared now, the solution is the square root of the right-hand side.
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Using a calculator you can find the sqrt of 10.
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Remember the sqrt term has both plus or minus values.
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Substitute the plus or minus values and solve to find the two zeroes (roots) for 'x'.
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Add 1 to both sides.

This defines the point: (-2.16227766016838, 0).
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Add 1 to both sides.

This defines the point: (4.16227766016838, 0).
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Looking back at the graph, you can see the parabola crosses the x-axis at these points.
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