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Question
Solve by completing the square:
x2 + 3x − 8 = 0
Sum
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Solution
Given:
x2 + 3x − 8 = 0
Move the constant to the right-hand side
x2 + 3x = 8
Complete the square
Coefficient of x = 3
Half = `3/2`
Square = `(3/2)^2 = 9/4`
`x^2 + 3x + 9/4 = 8+9/4`
`8 = 32/4`
`=> 32/4 + 9/4 = 41/4`
`= (x+3/2)^2 = 41/4`
`x + 3/2 = +- sqrt(41/4) = +- sqrt41/2`
`x = -3/2 +- sqrt41/2`
`x = (-3+-sqrt41)/2`
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