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Simplifying 104 = (2(x + 3))(x + -1) Reorder the terms: 104 = (2(3 + x))(x + -1) 104 = ((3 * 2 + x * 2))(x + -1) 104 = ((6 + 2x))(x + -1) Reorder the terms: 104 = (6 + 2x)(-1 + x) Multiply (6 + 2x) * (-1 + x) 104 = (6(-1 + x) + 2x * (-1 + x)) 104 = ((-1 * 6 + x * 6) + 2x * (-1 + x)) 104 = ((-6 + 6x) + 2x * (-1 + x)) 104 = (-6 + 6x + (-1 * 2x + x * 2x)) 104 = (-6 + 6x + (-2x + 2x2)) Combine like terms: 6x + -2x = 4x 104 = (-6 + 4x + 2x2) Solving 104 = -6 + 4x + 2x2 Solving for variable 'x'. Combine like terms: 104 + 6 = 110 110 + -4x + -2x2 = -6 + 4x + 2x2 + 6 + -4x + -2x2 Reorder the terms: 110 + -4x + -2x2 = -6 + 6 + 4x + -4x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 110 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2 110 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 110 + -4x + -2x2 = 0 + 2x2 + -2x2 110 + -4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 110 + -4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(55 + -2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(55 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 55 + -2x + -1x2 = 0 Solving 55 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -55 + 2x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + 2x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 2x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 2x + x2 = 0 + 55 2x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 2x + x2 = 55 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 = 55 + 1 Reorder the terms: 1 + 2x + x2 = 55 + 1 Combine like terms: 55 + 1 = 56 1 + 2x + x2 = 56 Factor a perfect square on the left side: (x + 1)(x + 1) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 1) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 1 = 7.483314774 Simplifying x + 1 = 7.483314774 Reorder the terms: 1 + x = 7.483314774 Solving 1 + x = 7.483314774 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 = 7.483314774 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.483314774 + -1 x = 7.483314774 + -1 Combine like terms: 7.483314774 + -1 = 6.483314774 x = 6.483314774 Simplifying x = 6.483314774Subproblem 2
x + 1 = -7.483314774 Simplifying x + 1 = -7.483314774 Reorder the terms: 1 + x = -7.483314774 Solving 1 + x = -7.483314774 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 = -7.483314774 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.483314774 + -1 x = -7.483314774 + -1 Combine like terms: -7.483314774 + -1 = -8.483314774 x = -8.483314774 Simplifying x = -8.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.483314774, -8.483314774}Solution
x = {6.483314774, -8.483314774}
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