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Simplifying 2X * X + 3X = 50 Multiply X * X 2X2 + 3X = 50 Reorder the terms: 3X + 2X2 = 50 Solving 3X + 2X2 = 50 Solving for variable 'X'. Reorder the terms: -50 + 3X + 2X2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 3X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25 + 1.5X + X2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 1.5X + 25 + X2 = 0 + 25 Reorder the terms: -25 + 25 + 1.5X + X2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 1.5X + X2 = 0 + 25 1.5X + X2 = 0 + 25 Combine like terms: 0 + 25 = 25 1.5X + X2 = 25 The X term is 1.5X. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5X + 0.5625 + X2 = 25 + 0.5625 Reorder the terms: 0.5625 + 1.5X + X2 = 25 + 0.5625 Combine like terms: 25 + 0.5625 = 25.5625 0.5625 + 1.5X + X2 = 25.5625 Factor a perfect square on the left side: (X + 0.75)(X + 0.75) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (X + 0.75) equal to 5.055937104 and -5.055937104.Subproblem 1
X + 0.75 = 5.055937104 Simplifying X + 0.75 = 5.055937104 Reorder the terms: 0.75 + X = 5.055937104 Solving 0.75 + X = 5.055937104 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + X = 5.055937104 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = 5.055937104 + -0.75 X = 5.055937104 + -0.75 Combine like terms: 5.055937104 + -0.75 = 4.305937104 X = 4.305937104 Simplifying X = 4.305937104Subproblem 2
X + 0.75 = -5.055937104 Simplifying X + 0.75 = -5.055937104 Reorder the terms: 0.75 + X = -5.055937104 Solving 0.75 + X = -5.055937104 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + X = -5.055937104 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = -5.055937104 + -0.75 X = -5.055937104 + -0.75 Combine like terms: -5.055937104 + -0.75 = -5.805937104 X = -5.805937104 Simplifying X = -5.805937104Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.305937104, -5.805937104}
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