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Simplifying 3X(4 + 2X) = 43 (4 * 3X + 2X * 3X) = 43 (12X + 6X2) = 43 Solving 12X + 6X2 = 43 Solving for variable 'X'. Reorder the terms: -43 + 12X + 6X2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + 12X + 6X2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -7.166666667 + 2X + X2 = 0 Move the constant term to the right: Add '7.166666667' to each side of the equation. -7.166666667 + 2X + 7.166666667 + X2 = 0 + 7.166666667 Reorder the terms: -7.166666667 + 7.166666667 + 2X + X2 = 0 + 7.166666667 Combine like terms: -7.166666667 + 7.166666667 = 0.000000000 0.000000000 + 2X + X2 = 0 + 7.166666667 2X + X2 = 0 + 7.166666667 Combine like terms: 0 + 7.166666667 = 7.166666667 2X + X2 = 7.166666667 The X term is 2X. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2X + 1 + X2 = 7.166666667 + 1 Reorder the terms: 1 + 2X + X2 = 7.166666667 + 1 Combine like terms: 7.166666667 + 1 = 8.166666667 1 + 2X + X2 = 8.166666667 Factor a perfect square on the left side: (X + 1)(X + 1) = 8.166666667 Calculate the square root of the right side: 2.857738033 Break this problem into two subproblems by setting (X + 1) equal to 2.857738033 and -2.857738033.Subproblem 1
X + 1 = 2.857738033 Simplifying X + 1 = 2.857738033 Reorder the terms: 1 + X = 2.857738033 Solving 1 + X = 2.857738033 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 2.857738033 + -1 Combine like terms: 1 + -1 = 0 0 + X = 2.857738033 + -1 X = 2.857738033 + -1 Combine like terms: 2.857738033 + -1 = 1.857738033 X = 1.857738033 Simplifying X = 1.857738033Subproblem 2
X + 1 = -2.857738033 Simplifying X + 1 = -2.857738033 Reorder the terms: 1 + X = -2.857738033 Solving 1 + X = -2.857738033 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -2.857738033 + -1 Combine like terms: 1 + -1 = 0 0 + X = -2.857738033 + -1 X = -2.857738033 + -1 Combine like terms: -2.857738033 + -1 = -3.857738033 X = -3.857738033 Simplifying X = -3.857738033Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.857738033, -3.857738033}
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