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Simplifying 72 = -32 + 16x + -2x2 + -32 Reorder the terms: 72 = -32 + -32 + 16x + -2x2 Combine like terms: -32 + -32 = -64 72 = -64 + 16x + -2x2 Solving 72 = -64 + 16x + -2x2 Solving for variable 'x'. Combine like terms: 72 + 64 = 136 136 + -16x + 2x2 = -64 + 16x + -2x2 + 64 + -16x + 2x2 Reorder the terms: 136 + -16x + 2x2 = -64 + 64 + 16x + -16x + -2x2 + 2x2 Combine like terms: -64 + 64 = 0 136 + -16x + 2x2 = 0 + 16x + -16x + -2x2 + 2x2 136 + -16x + 2x2 = 16x + -16x + -2x2 + 2x2 Combine like terms: 16x + -16x = 0 136 + -16x + 2x2 = 0 + -2x2 + 2x2 136 + -16x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 136 + -16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(68 + -8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(68 + -8x + x2)' equal to zero and attempt to solve: Simplifying 68 + -8x + x2 = 0 Solving 68 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-68' to each side of the equation. 68 + -8x + -68 + x2 = 0 + -68 Reorder the terms: 68 + -68 + -8x + x2 = 0 + -68 Combine like terms: 68 + -68 = 0 0 + -8x + x2 = 0 + -68 -8x + x2 = 0 + -68 Combine like terms: 0 + -68 = -68 -8x + x2 = -68 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -68 + 16 Reorder the terms: 16 + -8x + x2 = -68 + 16 Combine like terms: -68 + 16 = -52 16 + -8x + x2 = -52 Factor a perfect square on the left side: (x + -4)(x + -4) = -52 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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