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Simplifying 2x = [(4x + 16) + -4][(4x + 16) + -4] Reorder the terms: 2x = [(16 + 4x) + -4][(4x + 16) + -4] Remove parenthesis around (16 + 4x) 2x = [16 + 4x + -4][(4x + 16) + -4] Reorder the terms: 2x = [16 + -4 + 4x][(4x + 16) + -4] Combine like terms: 16 + -4 = 12 2x = [12 + 4x][(4x + 16) + -4] Reorder the terms: 2x = [12 + 4x][(16 + 4x) + -4] Remove parenthesis around (16 + 4x) 2x = [12 + 4x][16 + 4x + -4] Reorder the terms: 2x = [12 + 4x][16 + -4 + 4x] Combine like terms: 16 + -4 = 12 2x = [12 + 4x][12 + 4x] Multiply [12 + 4x] * [12 + 4x] 2x = [12[12 + 4x] + 4x * [12 + 4x]] 2x = [[12 * 12 + 4x * 12] + 4x * [12 + 4x]] 2x = [[144 + 48x] + 4x * [12 + 4x]] 2x = [144 + 48x + [12 * 4x + 4x * 4x]] 2x = [144 + 48x + [48x + 16x2]] Combine like terms: 48x + 48x = 96x 2x = [144 + 96x + 16x2] Solving 2x = 144 + 96x + 16x2 Solving for variable 'x'. Reorder the terms: -144 + 2x + -96x + -16x2 = 144 + 96x + 16x2 + -144 + -96x + -16x2 Combine like terms: 2x + -96x = -94x -144 + -94x + -16x2 = 144 + 96x + 16x2 + -144 + -96x + -16x2 Reorder the terms: -144 + -94x + -16x2 = 144 + -144 + 96x + -96x + 16x2 + -16x2 Combine like terms: 144 + -144 = 0 -144 + -94x + -16x2 = 0 + 96x + -96x + 16x2 + -16x2 -144 + -94x + -16x2 = 96x + -96x + 16x2 + -16x2 Combine like terms: 96x + -96x = 0 -144 + -94x + -16x2 = 0 + 16x2 + -16x2 -144 + -94x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -144 + -94x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(72 + 47x + 8x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(72 + 47x + 8x2)' equal to zero and attempt to solve: Simplifying 72 + 47x + 8x2 = 0 Solving 72 + 47x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 9 + 5.875x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + 5.875x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 5.875x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5.875x + x2 = 0 + -9 5.875x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 5.875x + x2 = -9 The x term is 5.875x. Take half its coefficient (2.9375). Square it (8.62890625) and add it to both sides. Add '8.62890625' to each side of the equation. 5.875x + 8.62890625 + x2 = -9 + 8.62890625 Reorder the terms: 8.62890625 + 5.875x + x2 = -9 + 8.62890625 Combine like terms: -9 + 8.62890625 = -0.37109375 8.62890625 + 5.875x + x2 = -0.37109375 Factor a perfect square on the left side: (x + 2.9375)(x + 2.9375) = -0.37109375 Can't calculate square root of the right side. 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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