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Simplifying 2x2 + -4x + -104 = 0 Reorder the terms: -104 + -4x + 2x2 = 0 Solving -104 + -4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-52 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-52 + -2x + x2)' equal to zero and attempt to solve: Simplifying -52 + -2x + x2 = 0 Solving -52 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -2x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -2x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -2x + x2 = 0 + 52 -2x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -2x + x2 = 52 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 52 + 1 Reorder the terms: 1 + -2x + x2 = 52 + 1 Combine like terms: 52 + 1 = 53 1 + -2x + x2 = 53 Factor a perfect square on the left side: (x + -1)(x + -1) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + -1) equal to 7.280109889 and -7.280109889.Subproblem 1
x + -1 = 7.280109889 Simplifying x + -1 = 7.280109889 Reorder the terms: -1 + x = 7.280109889 Solving -1 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7.280109889 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.280109889 + 1 x = 7.280109889 + 1 Combine like terms: 7.280109889 + 1 = 8.280109889 x = 8.280109889 Simplifying x = 8.280109889Subproblem 2
x + -1 = -7.280109889 Simplifying x + -1 = -7.280109889 Reorder the terms: -1 + x = -7.280109889 Solving -1 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7.280109889 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.280109889 + 1 x = -7.280109889 + 1 Combine like terms: -7.280109889 + 1 = -6.280109889 x = -6.280109889 Simplifying x = -6.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.280109889, -6.280109889}Solution
x = {8.280109889, -6.280109889}
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