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Simplifying 22X2 + 40.6X + -36 = 0 Reorder the terms: -36 + 40.6X + 22X2 = 0 Solving -36 + 40.6X + 22X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -1.636363636 + 1.845454545X + X2 = 0 Move the constant term to the right: Add '1.636363636' to each side of the equation. -1.636363636 + 1.845454545X + 1.636363636 + X2 = 0 + 1.636363636 Reorder the terms: -1.636363636 + 1.636363636 + 1.845454545X + X2 = 0 + 1.636363636 Combine like terms: -1.636363636 + 1.636363636 = 0.000000000 0.000000000 + 1.845454545X + X2 = 0 + 1.636363636 1.845454545X + X2 = 0 + 1.636363636 Combine like terms: 0 + 1.636363636 = 1.636363636 1.845454545X + X2 = 1.636363636 The X term is 1.845454545X. Take half its coefficient (0.9227272725). Square it (0.8514256194) and add it to both sides. Add '0.8514256194' to each side of the equation. 1.845454545X + 0.8514256194 + X2 = 1.636363636 + 0.8514256194 Reorder the terms: 0.8514256194 + 1.845454545X + X2 = 1.636363636 + 0.8514256194 Combine like terms: 1.636363636 + 0.8514256194 = 2.4877892554 0.8514256194 + 1.845454545X + X2 = 2.4877892554 Factor a perfect square on the left side: (X + 0.9227272725)(X + 0.9227272725) = 2.4877892554 Calculate the square root of the right side: 1.577272727 Break this problem into two subproblems by setting (X + 0.9227272725) equal to 1.577272727 and -1.577272727.Subproblem 1
X + 0.9227272725 = 1.577272727 Simplifying X + 0.9227272725 = 1.577272727 Reorder the terms: 0.9227272725 + X = 1.577272727 Solving 0.9227272725 + X = 1.577272727 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.9227272725' to each side of the equation. 0.9227272725 + -0.9227272725 + X = 1.577272727 + -0.9227272725 Combine like terms: 0.9227272725 + -0.9227272725 = 0.0000000000 0.0000000000 + X = 1.577272727 + -0.9227272725 X = 1.577272727 + -0.9227272725 Combine like terms: 1.577272727 + -0.9227272725 = 0.6545454545 X = 0.6545454545 Simplifying X = 0.6545454545Subproblem 2
X + 0.9227272725 = -1.577272727 Simplifying X + 0.9227272725 = -1.577272727 Reorder the terms: 0.9227272725 + X = -1.577272727 Solving 0.9227272725 + X = -1.577272727 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.9227272725' to each side of the equation. 0.9227272725 + -0.9227272725 + X = -1.577272727 + -0.9227272725 Combine like terms: 0.9227272725 + -0.9227272725 = 0.0000000000 0.0000000000 + X = -1.577272727 + -0.9227272725 X = -1.577272727 + -0.9227272725 Combine like terms: -1.577272727 + -0.9227272725 = -2.4999999995 X = -2.4999999995 Simplifying X = -2.4999999995Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.6545454545, -2.4999999995}
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