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Simplifying 56x2 + 2x4 = 104 Solving 56x2 + 2x4 = 104 Solving for variable 'x'. Reorder the terms: -104 + 56x2 + 2x4 = 104 + -104 Combine like terms: 104 + -104 = 0 -104 + 56x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-52 + 28x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-52 + 28x2 + x4)' equal to zero and attempt to solve: Simplifying -52 + 28x2 + x4 = 0 Solving -52 + 28x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 28x2 + 52 + x4 = 0 + 52 Reorder the terms: -52 + 52 + 28x2 + x4 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 28x2 + x4 = 0 + 52 28x2 + x4 = 0 + 52 Combine like terms: 0 + 52 = 52 28x2 + x4 = 52 The x term is 28x2. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x2 + 196 + x4 = 52 + 196 Reorder the terms: 196 + 28x2 + x4 = 52 + 196 Combine like terms: 52 + 196 = 248 196 + 28x2 + x4 = 248 Factor a perfect square on the left side: (x2 + 14)(x2 + 14) = 248 Calculate the square root of the right side: 15.748015748 Break this problem into two subproblems by setting (x2 + 14) equal to 15.748015748 and -15.748015748.Subproblem 1
x2 + 14 = 15.748015748 Simplifying x2 + 14 = 15.748015748 Reorder the terms: 14 + x2 = 15.748015748 Solving 14 + x2 = 15.748015748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x2 = 15.748015748 + -14 Combine like terms: 14 + -14 = 0 0 + x2 = 15.748015748 + -14 x2 = 15.748015748 + -14 Combine like terms: 15.748015748 + -14 = 1.748015748 x2 = 1.748015748 Simplifying x2 = 1.748015748 Take the square root of each side: x = {-1.322125466, 1.322125466}Subproblem 2
x2 + 14 = -15.748015748 Simplifying x2 + 14 = -15.748015748 Reorder the terms: 14 + x2 = -15.748015748 Solving 14 + x2 = -15.748015748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x2 = -15.748015748 + -14 Combine like terms: 14 + -14 = 0 0 + x2 = -15.748015748 + -14 x2 = -15.748015748 + -14 Combine like terms: -15.748015748 + -14 = -29.748015748 x2 = -29.748015748 Simplifying x2 = -29.748015748 Reorder the terms: 29.748015748 + x2 = -29.748015748 + 29.748015748 Combine like terms: -29.748015748 + 29.748015748 = 0.000000000 29.748015748 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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