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Simplifying 2x2 + 6x + -194 = 0 Reorder the terms: -194 + 6x + 2x2 = 0 Solving -194 + 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-97 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-97 + 3x + x2)' equal to zero and attempt to solve: Simplifying -97 + 3x + x2 = 0 Solving -97 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + 3x + 97 + x2 = 0 + 97 Reorder the terms: -97 + 97 + 3x + x2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + 3x + x2 = 0 + 97 3x + x2 = 0 + 97 Combine like terms: 0 + 97 = 97 3x + x2 = 97 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 97 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 97 + 2.25 Combine like terms: 97 + 2.25 = 99.25 2.25 + 3x + x2 = 99.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 99.25 Calculate the square root of the right side: 9.962429423 Break this problem into two subproblems by setting (x + 1.5) equal to 9.962429423 and -9.962429423.Subproblem 1
x + 1.5 = 9.962429423 Simplifying x + 1.5 = 9.962429423 Reorder the terms: 1.5 + x = 9.962429423 Solving 1.5 + x = 9.962429423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.962429423 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.962429423 + -1.5 x = 9.962429423 + -1.5 Combine like terms: 9.962429423 + -1.5 = 8.462429423 x = 8.462429423 Simplifying x = 8.462429423Subproblem 2
x + 1.5 = -9.962429423 Simplifying x + 1.5 = -9.962429423 Reorder the terms: 1.5 + x = -9.962429423 Solving 1.5 + x = -9.962429423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.962429423 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.962429423 + -1.5 x = -9.962429423 + -1.5 Combine like terms: -9.962429423 + -1.5 = -11.462429423 x = -11.462429423 Simplifying x = -11.462429423Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.462429423, -11.462429423}Solution
x = {8.462429423, -11.462429423}
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