Solve for X:x^2+5x-(a^2+a-6) step by step explanation
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Step-by-step explanation:
x² + 5x - (a² + a - 6) = 0
//first factorize a² + a - 6
=> x² + 5x - (a² + 3a - 2a - 6) = 0
=> x² + 5x - (a ( a + 3 ) - 2( a +3)) = 0
=> x² + 5x - (a + 3)(a - 2) = 0
//Now factorize again, 5 can be written as 5 = [ (a + 3) - (a - 2)]
=> x² + [(a+3) - (a - 2)]x - (a + 3)(a - 2) = 0
=> x² + (a+3)x - (a-2x) - (a + 3)(a - 2) = 0
=> x (x + (a+3)) - (a-2) (x + (a+3)) = 0
=> [x + (a+3)] [x - (a-2)] = 0
=> x + (a+3) = 0 or x - (a-2) = 0
=> x = - (a+3) or x = (a - 2)
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