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Simplifying 4x2 + -420x + -2744 = 0 Reorder the terms: -2744 + -420x + 4x2 = 0 Solving -2744 + -420x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-686 + -105x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-686 + -105x + x2)' equal to zero and attempt to solve: Simplifying -686 + -105x + x2 = 0 Solving -686 + -105x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '686' to each side of the equation. -686 + -105x + 686 + x2 = 0 + 686 Reorder the terms: -686 + 686 + -105x + x2 = 0 + 686 Combine like terms: -686 + 686 = 0 0 + -105x + x2 = 0 + 686 -105x + x2 = 0 + 686 Combine like terms: 0 + 686 = 686 -105x + x2 = 686 The x term is -105x. Take half its coefficient (-52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. -105x + 2756.25 + x2 = 686 + 2756.25 Reorder the terms: 2756.25 + -105x + x2 = 686 + 2756.25 Combine like terms: 686 + 2756.25 = 3442.25 2756.25 + -105x + x2 = 3442.25 Factor a perfect square on the left side: (x + -52.5)(x + -52.5) = 3442.25 Calculate the square root of the right side: 58.67069115 Break this problem into two subproblems by setting (x + -52.5) equal to 58.67069115 and -58.67069115.Subproblem 1
x + -52.5 = 58.67069115 Simplifying x + -52.5 = 58.67069115 Reorder the terms: -52.5 + x = 58.67069115 Solving -52.5 + x = 58.67069115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + x = 58.67069115 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x = 58.67069115 + 52.5 x = 58.67069115 + 52.5 Combine like terms: 58.67069115 + 52.5 = 111.17069115 x = 111.17069115 Simplifying x = 111.17069115Subproblem 2
x + -52.5 = -58.67069115 Simplifying x + -52.5 = -58.67069115 Reorder the terms: -52.5 + x = -58.67069115 Solving -52.5 + x = -58.67069115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + x = -58.67069115 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x = -58.67069115 + 52.5 x = -58.67069115 + 52.5 Combine like terms: -58.67069115 + 52.5 = -6.17069115 x = -6.17069115 Simplifying x = -6.17069115Solution
The solution to the problem is based on the solutions from the subproblems. x = {111.17069115, -6.17069115}Solution
x = {111.17069115, -6.17069115}
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