find the roots of the following quadratic equation if they exist by the method of completing the square. x square + X - 4 =0
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Hi ,
x² + x - 4 = 0
=> x² + x = 4
=> x² + 2 × x × 1/2 = 4
=> x² + 2 × x × 1/2 + ( 1/2 )² = 4 + ( 1/2 )²
=> ( x + 1/2 )² = 4 + 1/4
=> ( x + 1/2 )² = ( 16 + 1 )/4
=> ( x + 1/2 )² = 17/4
=> ( x + 1/2 )= ± √17/2
x = -1/2 ± √17/2
x = ( -1 ± √17 )/2
Therefore ,
x = ( -1 + √17 )/2 or x = ( -1 - √17 )/2
I hope this helps you.
: )
x² + x - 4 = 0
=> x² + x = 4
=> x² + 2 × x × 1/2 = 4
=> x² + 2 × x × 1/2 + ( 1/2 )² = 4 + ( 1/2 )²
=> ( x + 1/2 )² = 4 + 1/4
=> ( x + 1/2 )² = ( 16 + 1 )/4
=> ( x + 1/2 )² = 17/4
=> ( x + 1/2 )= ± √17/2
x = -1/2 ± √17/2
x = ( -1 ± √17 )/2
Therefore ,
x = ( -1 + √17 )/2 or x = ( -1 - √17 )/2
I hope this helps you.
: )
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