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Simplifying 2x2 + 32x + 104 = 0 Reorder the terms: 104 + 32x + 2x2 = 0 Solving 104 + 32x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(52 + 16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(52 + 16x + x2)' equal to zero and attempt to solve: Simplifying 52 + 16x + x2 = 0 Solving 52 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + 16x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + 16x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + 16x + x2 = 0 + -52 16x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 16x + x2 = -52 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -52 + 64 Reorder the terms: 64 + 16x + x2 = -52 + 64 Combine like terms: -52 + 64 = 12 64 + 16x + x2 = 12 Factor a perfect square on the left side: (x + 8)(x + 8) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 8) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 8 = 3.464101615 Simplifying x + 8 = 3.464101615 Reorder the terms: 8 + x = 3.464101615 Solving 8 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 3.464101615 + -8 Combine like terms: 8 + -8 = 0 0 + x = 3.464101615 + -8 x = 3.464101615 + -8 Combine like terms: 3.464101615 + -8 = -4.535898385 x = -4.535898385 Simplifying x = -4.535898385Subproblem 2
x + 8 = -3.464101615 Simplifying x + 8 = -3.464101615 Reorder the terms: 8 + x = -3.464101615 Solving 8 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -3.464101615 + -8 Combine like terms: 8 + -8 = 0 0 + x = -3.464101615 + -8 x = -3.464101615 + -8 Combine like terms: -3.464101615 + -8 = -11.464101615 x = -11.464101615 Simplifying x = -11.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.535898385, -11.464101615}Solution
x = {-4.535898385, -11.464101615}
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