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Step one: move the constant to the other side x2 + 8x - 9 = 0 x2 + 8x = x2 + 8x + ( Step two: 'Complete the square'. (halve the co-efficient of the x, square it, add to both sides) x2 + 8x = 9 )2 = 9 + ( )2 x2 + 8x +(4)2 = 9 + (4)2 Step three: You have created a 'square' on the left. Show it and simplify the right. ( x + )2 = Step four: Get the square root of both sides, then solve for x. (x + 4)2 = 25 x + 4 = ±√ x = - x + 4 = ±√25 x = or x = ± BRING ON THE FRACTIONS Step one: move the constant to the other side x2 - 5x + 2 = 0 x2 - 5x = x2 - 5x +(- Step two: 'Complete the square'. (halve the co-efficient of the x, square it, add to both sides) x2 - 5x = -2 )2 = -2 +(- )2 x2 - 5x +(-5)2 = -2 + (-5)2 Step three: You have created a 'square' on the left. Show it and simplify the right. (x - 5)2 = -2 + 2 2 2 (x - 5)2 = -2 + 25 (x - 5)2 = 2 2 4 Step four: Get the square root of both sides, then solve for x. (x - 5)2 = 17 x - 5 = ±√ 2 2 4 x - 5 = ±√17 x - 5 = ±√ 2 2 4 x - 5 = ±√17 x = ±√17 2 2 2 |