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Simplifying 5X(X + 1) = 2X + 17 Reorder the terms: 5X(1 + X) = 2X + 17 (1 * 5X + X * 5X) = 2X + 17 (5X + 5X2) = 2X + 17 Reorder the terms: 5X + 5X2 = 17 + 2X Solving 5X + 5X2 = 17 + 2X Solving for variable 'X'. Reorder the terms: -17 + 5X + -2X + 5X2 = 17 + 2X + -17 + -2X Combine like terms: 5X + -2X = 3X -17 + 3X + 5X2 = 17 + 2X + -17 + -2X Reorder the terms: -17 + 3X + 5X2 = 17 + -17 + 2X + -2X Combine like terms: 17 + -17 = 0 -17 + 3X + 5X2 = 0 + 2X + -2X -17 + 3X + 5X2 = 2X + -2X Combine like terms: 2X + -2X = 0 -17 + 3X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + 0.6X + X2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + 0.6X + 3.4 + X2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + 0.6X + X2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + 0.6X + X2 = 0 + 3.4 0.6X + X2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 0.6X + X2 = 3.4 The X term is 0.6X. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6X + 0.09 + X2 = 3.4 + 0.09 Reorder the terms: 0.09 + 0.6X + X2 = 3.4 + 0.09 Combine like terms: 3.4 + 0.09 = 3.49 0.09 + 0.6X + X2 = 3.49 Factor a perfect square on the left side: (X + 0.3)(X + 0.3) = 3.49 Calculate the square root of the right side: 1.868154169 Break this problem into two subproblems by setting (X + 0.3) equal to 1.868154169 and -1.868154169.Subproblem 1
X + 0.3 = 1.868154169 Simplifying X + 0.3 = 1.868154169 Reorder the terms: 0.3 + X = 1.868154169 Solving 0.3 + X = 1.868154169 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + X = 1.868154169 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + X = 1.868154169 + -0.3 X = 1.868154169 + -0.3 Combine like terms: 1.868154169 + -0.3 = 1.568154169 X = 1.568154169 Simplifying X = 1.568154169Subproblem 2
X + 0.3 = -1.868154169 Simplifying X + 0.3 = -1.868154169 Reorder the terms: 0.3 + X = -1.868154169 Solving 0.3 + X = -1.868154169 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + X = -1.868154169 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + X = -1.868154169 + -0.3 X = -1.868154169 + -0.3 Combine like terms: -1.868154169 + -0.3 = -2.168154169 X = -2.168154169 Simplifying X = -2.168154169Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.568154169, -2.168154169}
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