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Simplifying 2x2 + 14x + -2014 = 0 Reorder the terms: -2014 + 14x + 2x2 = 0 Solving -2014 + 14x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1007 + 7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1007 + 7x + x2)' equal to zero and attempt to solve: Simplifying -1007 + 7x + x2 = 0 Solving -1007 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1007' to each side of the equation. -1007 + 7x + 1007 + x2 = 0 + 1007 Reorder the terms: -1007 + 1007 + 7x + x2 = 0 + 1007 Combine like terms: -1007 + 1007 = 0 0 + 7x + x2 = 0 + 1007 7x + x2 = 0 + 1007 Combine like terms: 0 + 1007 = 1007 7x + x2 = 1007 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 1007 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 1007 + 12.25 Combine like terms: 1007 + 12.25 = 1019.25 12.25 + 7x + x2 = 1019.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 1019.25 Calculate the square root of the right side: 31.925694981 Break this problem into two subproblems by setting (x + 3.5) equal to 31.925694981 and -31.925694981.Subproblem 1
x + 3.5 = 31.925694981 Simplifying x + 3.5 = 31.925694981 Reorder the terms: 3.5 + x = 31.925694981 Solving 3.5 + x = 31.925694981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 31.925694981 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 31.925694981 + -3.5 x = 31.925694981 + -3.5 Combine like terms: 31.925694981 + -3.5 = 28.425694981 x = 28.425694981 Simplifying x = 28.425694981Subproblem 2
x + 3.5 = -31.925694981 Simplifying x + 3.5 = -31.925694981 Reorder the terms: 3.5 + x = -31.925694981 Solving 3.5 + x = -31.925694981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -31.925694981 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -31.925694981 + -3.5 x = -31.925694981 + -3.5 Combine like terms: -31.925694981 + -3.5 = -35.425694981 x = -35.425694981 Simplifying x = -35.425694981Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.425694981, -35.425694981}Solution
x = {28.425694981, -35.425694981}
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