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Simplifying 50x2 + -15x + -2 = (5x + 2) Reorder the terms: -2 + -15x + 50x2 = (5x + 2) Reorder the terms: -2 + -15x + 50x2 = (2 + 5x) Remove parenthesis around (2 + 5x) -2 + -15x + 50x2 = 2 + 5x Solving -2 + -15x + 50x2 = 2 + 5x Solving for variable 'x'. Reorder the terms: -2 + -2 + -15x + -5x + 50x2 = 2 + 5x + -2 + -5x Combine like terms: -2 + -2 = -4 -4 + -15x + -5x + 50x2 = 2 + 5x + -2 + -5x Combine like terms: -15x + -5x = -20x -4 + -20x + 50x2 = 2 + 5x + -2 + -5x Reorder the terms: -4 + -20x + 50x2 = 2 + -2 + 5x + -5x Combine like terms: 2 + -2 = 0 -4 + -20x + 50x2 = 0 + 5x + -5x -4 + -20x + 50x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -4 + -20x + 50x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -10x + 25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -10x + 25x2)' equal to zero and attempt to solve: Simplifying -2 + -10x + 25x2 = 0 Solving -2 + -10x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.08 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + -0.4x + 0.08 + x2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + -0.4x + x2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + -0.4x + x2 = 0 + 0.08 -0.4x + x2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 -0.4x + x2 = 0.08 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.08 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.08 + 0.04 Combine like terms: 0.08 + 0.04 = 0.12 0.04 + -0.4x + x2 = 0.12 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.12 Calculate the square root of the right side: 0.346410162 Break this problem into two subproblems by setting (x + -0.2) equal to 0.346410162 and -0.346410162.Subproblem 1
x + -0.2 = 0.346410162 Simplifying x + -0.2 = 0.346410162 Reorder the terms: -0.2 + x = 0.346410162 Solving -0.2 + x = 0.346410162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.346410162 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.346410162 + 0.2 x = 0.346410162 + 0.2 Combine like terms: 0.346410162 + 0.2 = 0.546410162 x = 0.546410162 Simplifying x = 0.546410162Subproblem 2
x + -0.2 = -0.346410162 Simplifying x + -0.2 = -0.346410162 Reorder the terms: -0.2 + x = -0.346410162 Solving -0.2 + x = -0.346410162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.346410162 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.346410162 + 0.2 x = -0.346410162 + 0.2 Combine like terms: -0.346410162 + 0.2 = -0.146410162 x = -0.146410162 Simplifying x = -0.146410162Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.546410162, -0.146410162}Solution
x = {0.546410162, -0.146410162}
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