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Simplifying 2x2 + -20x + -42 = 0 Reorder the terms: -42 + -20x + 2x2 = 0 Solving -42 + -20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -10x + x2)' equal to zero and attempt to solve: Simplifying -21 + -10x + x2 = 0 Solving -21 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -10x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -10x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -10x + x2 = 0 + 21 -10x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -10x + x2 = 21 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 21 + 25 Reorder the terms: 25 + -10x + x2 = 21 + 25 Combine like terms: 21 + 25 = 46 25 + -10x + x2 = 46 Factor a perfect square on the left side: (x + -5)(x + -5) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + -5) equal to 6.782329983 and -6.782329983.Subproblem 1
x + -5 = 6.782329983 Simplifying x + -5 = 6.782329983 Reorder the terms: -5 + x = 6.782329983 Solving -5 + x = 6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.782329983 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.782329983 + 5 x = 6.782329983 + 5 Combine like terms: 6.782329983 + 5 = 11.782329983 x = 11.782329983 Simplifying x = 11.782329983Subproblem 2
x + -5 = -6.782329983 Simplifying x + -5 = -6.782329983 Reorder the terms: -5 + x = -6.782329983 Solving -5 + x = -6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.782329983 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.782329983 + 5 x = -6.782329983 + 5 Combine like terms: -6.782329983 + 5 = -1.782329983 x = -1.782329983 Simplifying x = -1.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.782329983, -1.782329983}Solution
x = {11.782329983, -1.782329983}
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