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Simplifying 3x2 + -147x + -102 = 0 Reorder the terms: -102 + -147x + 3x2 = 0 Solving -102 + -147x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-34 + -49x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-34 + -49x + x2)' equal to zero and attempt to solve: Simplifying -34 + -49x + x2 = 0 Solving -34 + -49x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -49x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -49x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -49x + x2 = 0 + 34 -49x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -49x + x2 = 34 The x term is -49x. Take half its coefficient (-24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. -49x + 600.25 + x2 = 34 + 600.25 Reorder the terms: 600.25 + -49x + x2 = 34 + 600.25 Combine like terms: 34 + 600.25 = 634.25 600.25 + -49x + x2 = 634.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 634.25 Calculate the square root of the right side: 25.184320519 Break this problem into two subproblems by setting (x + -24.5) equal to 25.184320519 and -25.184320519.Subproblem 1
x + -24.5 = 25.184320519 Simplifying x + -24.5 = 25.184320519 Reorder the terms: -24.5 + x = 25.184320519 Solving -24.5 + x = 25.184320519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = 25.184320519 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 25.184320519 + 24.5 x = 25.184320519 + 24.5 Combine like terms: 25.184320519 + 24.5 = 49.684320519 x = 49.684320519 Simplifying x = 49.684320519Subproblem 2
x + -24.5 = -25.184320519 Simplifying x + -24.5 = -25.184320519 Reorder the terms: -24.5 + x = -25.184320519 Solving -24.5 + x = -25.184320519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = -25.184320519 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -25.184320519 + 24.5 x = -25.184320519 + 24.5 Combine like terms: -25.184320519 + 24.5 = -0.684320519 x = -0.684320519 Simplifying x = -0.684320519Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.684320519, -0.684320519}Solution
x = {49.684320519, -0.684320519}
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