Complete the square and write in graphing form.

Question

2x^2=5x+12

Answer 1

2 x ^ 2 = 5 x + 12

Subtract 5 x + 12 to both sides

2 x ^ 2 - ( 5 x + 12 ) = 5 x + 12 - ( 5 x + 12 )

2 x ^ 2 - 5 x - 12 = 0 Divide both sides by leading coefficient ( 2 )

x ^ 2 - 5 x / 2 - 6 = 0 Add 6 to both sides

x ^ 2 - 5 x / 2 - 6 + 6 = 0 + 6

x ^ 2 - 5 x / 2 = 6

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Take one half of the coefficient of x and square it.

In this case [ ( 5 / 2 ) / 2 ] ^ 2 = ( 5 / 4 ) ^ 2 = 25 / 16
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Add 25 / 16 to both sides

x ^ 2 - 5 x / 2 + 25 / 16 = 6 + 25 / 16

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Remark :

x ^ 2 - 5 x / 2 + 25 / 16 = ( x - 5 / 4 ) ^ 2

6 = 96 / 16
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( x - 5 / 4 ) ^ 2 = 96 / 16 + 25 / 16

( x - 5 / 4 ) ^ 2 = 121 / 16

x - 5 / 4 = + OR - sqrt ( 121 / 16 )

x - 5 / 4 = + OR - 11 / 4 Add 5 / 4 to both sides

x - 5 / 4 + 5 / 4 = + OR - 11 / 4 + 5 / 4

x = + OR - 11 / 4 + 5 / 4

x1 = 11 / 4 + 5 / 4 = 16 / 4 = 4

x2 = - 11 / 4 + 5 / 4 = - 6 / 4 = - 3 / 2

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2 x ^ 2 = 5 x + 12

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