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Simplifying 1.9(X2 + -3X + 2) = X2 Reorder the terms: 1.9(2 + -3X + X2) = X2 (2 * 1.9 + -3X * 1.9 + X2 * 1.9) = X2 (3.8 + -5.7X + 1.9X2) = X2 Solving 3.8 + -5.7X + 1.9X2 = X2 Solving for variable 'X'. Combine like terms: 1.9X2 + -1X2 = 0.9X2 3.8 + -5.7X + 0.9X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 3.8 + -5.7X + 0.9X2 = 0 Begin completing the square. Divide all terms by 0.9 the coefficient of the squared term: Divide each side by '0.9'. 4.222222222 + -6.333333333X + X2 = 0 Move the constant term to the right: Add '-4.222222222' to each side of the equation. 4.222222222 + -6.333333333X + -4.222222222 + X2 = 0 + -4.222222222 Reorder the terms: 4.222222222 + -4.222222222 + -6.333333333X + X2 = 0 + -4.222222222 Combine like terms: 4.222222222 + -4.222222222 = 0.000000000 0.000000000 + -6.333333333X + X2 = 0 + -4.222222222 -6.333333333X + X2 = 0 + -4.222222222 Combine like terms: 0 + -4.222222222 = -4.222222222 -6.333333333X + X2 = -4.222222222 The X term is -6.333333333X. Take half its coefficient (-3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. -6.333333333X + 10.02777778 + X2 = -4.222222222 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333X + X2 = -4.222222222 + 10.02777778 Combine like terms: -4.222222222 + 10.02777778 = 5.805555558 10.02777778 + -6.333333333X + X2 = 5.805555558 Factor a perfect square on the left side: (X + -3.166666667)(X + -3.166666667) = 5.805555558 Calculate the square root of the right side: 2.40947205 Break this problem into two subproblems by setting (X + -3.166666667) equal to 2.40947205 and -2.40947205.Subproblem 1
X + -3.166666667 = 2.40947205 Simplifying X + -3.166666667 = 2.40947205 Reorder the terms: -3.166666667 + X = 2.40947205 Solving -3.166666667 + X = 2.40947205 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + X = 2.40947205 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + X = 2.40947205 + 3.166666667 X = 2.40947205 + 3.166666667 Combine like terms: 2.40947205 + 3.166666667 = 5.576138717 X = 5.576138717 Simplifying X = 5.576138717Subproblem 2
X + -3.166666667 = -2.40947205 Simplifying X + -3.166666667 = -2.40947205 Reorder the terms: -3.166666667 + X = -2.40947205 Solving -3.166666667 + X = -2.40947205 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + X = -2.40947205 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + X = -2.40947205 + 3.166666667 X = -2.40947205 + 3.166666667 Combine like terms: -2.40947205 + 3.166666667 = 0.757194617 X = 0.757194617 Simplifying X = 0.757194617Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.576138717, 0.757194617}
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