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Simplifying 2x2 + 4x + 49 = 169 Reorder the terms: 49 + 4x + 2x2 = 169 Solving 49 + 4x + 2x2 = 169 Solving for variable 'x'. Reorder the terms: 49 + -169 + 4x + 2x2 = 169 + -169 Combine like terms: 49 + -169 = -120 -120 + 4x + 2x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -120 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + 2x + x2)' equal to zero and attempt to solve: Simplifying -60 + 2x + x2 = 0 Solving -60 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 2x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 2x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 2x + x2 = 0 + 60 2x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 2x + x2 = 60 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 = 60 + 1 Reorder the terms: 1 + 2x + x2 = 60 + 1 Combine like terms: 60 + 1 = 61 1 + 2x + x2 = 61 Factor a perfect square on the left side: (x + 1)(x + 1) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + 1) equal to 7.810249676 and -7.810249676.Subproblem 1
x + 1 = 7.810249676 Simplifying x + 1 = 7.810249676 Reorder the terms: 1 + x = 7.810249676 Solving 1 + x = 7.810249676 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 = 7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.810249676 + -1 x = 7.810249676 + -1 Combine like terms: 7.810249676 + -1 = 6.810249676 x = 6.810249676 Simplifying x = 6.810249676Subproblem 2
x + 1 = -7.810249676 Simplifying x + 1 = -7.810249676 Reorder the terms: 1 + x = -7.810249676 Solving 1 + x = -7.810249676 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 = -7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.810249676 + -1 x = -7.810249676 + -1 Combine like terms: -7.810249676 + -1 = -8.810249676 x = -8.810249676 Simplifying x = -8.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.810249676, -8.810249676}Solution
x = {6.810249676, -8.810249676}
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