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Simplifying X[2X + 3] = 100 Reorder the terms: X[3 + 2X] = 100 [3 * X + 2X * X] = 100 [3X + 2X2] = 100 Solving 3X + 2X2 = 100 Solving for variable 'X'. Reorder the terms: -100 + 3X + 2X2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 3X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + 1.5X + X2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 1.5X + 50 + X2 = 0 + 50 Reorder the terms: -50 + 50 + 1.5X + X2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 1.5X + X2 = 0 + 50 1.5X + X2 = 0 + 50 Combine like terms: 0 + 50 = 50 1.5X + X2 = 50 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 = 50 + 0.5625 Reorder the terms: 0.5625 + 1.5X + X2 = 50 + 0.5625 Combine like terms: 50 + 0.5625 = 50.5625 0.5625 + 1.5X + X2 = 50.5625 Factor a perfect square on the left side: (X + 0.75)(X + 0.75) = 50.5625 Calculate the square root of the right side: 7.110731327 Break this problem into two subproblems by setting (X + 0.75) equal to 7.110731327 and -7.110731327.Subproblem 1
X + 0.75 = 7.110731327 Simplifying X + 0.75 = 7.110731327 Reorder the terms: 0.75 + X = 7.110731327 Solving 0.75 + X = 7.110731327 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 = 7.110731327 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = 7.110731327 + -0.75 X = 7.110731327 + -0.75 Combine like terms: 7.110731327 + -0.75 = 6.360731327 X = 6.360731327 Simplifying X = 6.360731327Subproblem 2
X + 0.75 = -7.110731327 Simplifying X + 0.75 = -7.110731327 Reorder the terms: 0.75 + X = -7.110731327 Solving 0.75 + X = -7.110731327 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 = -7.110731327 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = -7.110731327 + -0.75 X = -7.110731327 + -0.75 Combine like terms: -7.110731327 + -0.75 = -7.860731327 X = -7.860731327 Simplifying X = -7.860731327Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.360731327, -7.860731327}
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