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Simplifying -1.2X + -0.22X2 + 1.01 = 0 Reorder the terms: 1.01 + -1.2X + -0.22X2 = 0 Solving 1.01 + -1.2X + -0.22X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -0.22 the coefficient of the squared term: Divide each side by '-0.22'. -4.590909091 + 5.454545455X + X2 = 0 Move the constant term to the right: Add '4.590909091' to each side of the equation. -4.590909091 + 5.454545455X + 4.590909091 + X2 = 0 + 4.590909091 Reorder the terms: -4.590909091 + 4.590909091 + 5.454545455X + X2 = 0 + 4.590909091 Combine like terms: -4.590909091 + 4.590909091 = 0.000000000 0.000000000 + 5.454545455X + X2 = 0 + 4.590909091 5.454545455X + X2 = 0 + 4.590909091 Combine like terms: 0 + 4.590909091 = 4.590909091 5.454545455X + X2 = 4.590909091 The X term is 5.454545455X. Take half its coefficient (2.727272728). Square it (7.438016533) and add it to both sides. Add '7.438016533' to each side of the equation. 5.454545455X + 7.438016533 + X2 = 4.590909091 + 7.438016533 Reorder the terms: 7.438016533 + 5.454545455X + X2 = 4.590909091 + 7.438016533 Combine like terms: 4.590909091 + 7.438016533 = 12.028925624 7.438016533 + 5.454545455X + X2 = 12.028925624 Factor a perfect square on the left side: (X + 2.727272728)(X + 2.727272728) = 12.028925624 Calculate the square root of the right side: 3.468274156 Break this problem into two subproblems by setting (X + 2.727272728) equal to 3.468274156 and -3.468274156.Subproblem 1
X + 2.727272728 = 3.468274156 Simplifying X + 2.727272728 = 3.468274156 Reorder the terms: 2.727272728 + X = 3.468274156 Solving 2.727272728 + X = 3.468274156 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.727272728' to each side of the equation. 2.727272728 + -2.727272728 + X = 3.468274156 + -2.727272728 Combine like terms: 2.727272728 + -2.727272728 = 0.000000000 0.000000000 + X = 3.468274156 + -2.727272728 X = 3.468274156 + -2.727272728 Combine like terms: 3.468274156 + -2.727272728 = 0.741001428 X = 0.741001428 Simplifying X = 0.741001428Subproblem 2
X + 2.727272728 = -3.468274156 Simplifying X + 2.727272728 = -3.468274156 Reorder the terms: 2.727272728 + X = -3.468274156 Solving 2.727272728 + X = -3.468274156 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.727272728' to each side of the equation. 2.727272728 + -2.727272728 + X = -3.468274156 + -2.727272728 Combine like terms: 2.727272728 + -2.727272728 = 0.000000000 0.000000000 + X = -3.468274156 + -2.727272728 X = -3.468274156 + -2.727272728 Combine like terms: -3.468274156 + -2.727272728 = -6.195546884 X = -6.195546884 Simplifying X = -6.195546884Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.741001428, -6.195546884}
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