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Simplifying 5X(X + 10) = 3(5X + -6) Reorder the terms: 5X(10 + X) = 3(5X + -6) (10 * 5X + X * 5X) = 3(5X + -6) (50X + 5X2) = 3(5X + -6) Reorder the terms: 50X + 5X2 = 3(-6 + 5X) 50X + 5X2 = (-6 * 3 + 5X * 3) 50X + 5X2 = (-18 + 15X) Solving 50X + 5X2 = -18 + 15X Solving for variable 'X'. Reorder the terms: 18 + 50X + -15X + 5X2 = -18 + 15X + 18 + -15X Combine like terms: 50X + -15X = 35X 18 + 35X + 5X2 = -18 + 15X + 18 + -15X Reorder the terms: 18 + 35X + 5X2 = -18 + 18 + 15X + -15X Combine like terms: -18 + 18 = 0 18 + 35X + 5X2 = 0 + 15X + -15X 18 + 35X + 5X2 = 15X + -15X Combine like terms: 15X + -15X = 0 18 + 35X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.6 + 7X + X2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + 7X + -3.6 + X2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + 7X + X2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + 7X + X2 = 0 + -3.6 7X + X2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 7X + X2 = -3.6 The X term is 7X. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7X + 12.25 + X2 = -3.6 + 12.25 Reorder the terms: 12.25 + 7X + X2 = -3.6 + 12.25 Combine like terms: -3.6 + 12.25 = 8.65 12.25 + 7X + X2 = 8.65 Factor a perfect square on the left side: (X + 3.5)(X + 3.5) = 8.65 Calculate the square root of the right side: 2.941088234 Break this problem into two subproblems by setting (X + 3.5) equal to 2.941088234 and -2.941088234.Subproblem 1
X + 3.5 = 2.941088234 Simplifying X + 3.5 = 2.941088234 Reorder the terms: 3.5 + X = 2.941088234 Solving 3.5 + X = 2.941088234 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + X = 2.941088234 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + X = 2.941088234 + -3.5 X = 2.941088234 + -3.5 Combine like terms: 2.941088234 + -3.5 = -0.558911766 X = -0.558911766 Simplifying X = -0.558911766Subproblem 2
X + 3.5 = -2.941088234 Simplifying X + 3.5 = -2.941088234 Reorder the terms: 3.5 + X = -2.941088234 Solving 3.5 + X = -2.941088234 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + X = -2.941088234 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + X = -2.941088234 + -3.5 X = -2.941088234 + -3.5 Combine like terms: -2.941088234 + -3.5 = -6.441088234 X = -6.441088234 Simplifying X = -6.441088234Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.558911766, -6.441088234}
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