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Simplifying 4x + -12 + 2x + 8 = x2 + 10x + 28 Reorder the terms: -12 + 8 + 4x + 2x = x2 + 10x + 28 Combine like terms: -12 + 8 = -4 -4 + 4x + 2x = x2 + 10x + 28 Combine like terms: 4x + 2x = 6x -4 + 6x = x2 + 10x + 28 Reorder the terms: -4 + 6x = 28 + 10x + x2 Solving -4 + 6x = 28 + 10x + x2 Solving for variable 'x'. Reorder the terms: -4 + -28 + 6x + -10x + -1x2 = 28 + 10x + x2 + -28 + -10x + -1x2 Combine like terms: -4 + -28 = -32 -32 + 6x + -10x + -1x2 = 28 + 10x + x2 + -28 + -10x + -1x2 Combine like terms: 6x + -10x = -4x -32 + -4x + -1x2 = 28 + 10x + x2 + -28 + -10x + -1x2 Reorder the terms: -32 + -4x + -1x2 = 28 + -28 + 10x + -10x + x2 + -1x2 Combine like terms: 28 + -28 = 0 -32 + -4x + -1x2 = 0 + 10x + -10x + x2 + -1x2 -32 + -4x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -32 + -4x + -1x2 = 0 + x2 + -1x2 -32 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -32 + -4x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(32 + 4x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(32 + 4x + x2)' equal to zero and attempt to solve: Simplifying 32 + 4x + x2 = 0 Solving 32 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 4x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 4x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 4x + x2 = 0 + -32 4x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 4x + x2 = -32 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -32 + 4 Reorder the terms: 4 + 4x + x2 = -32 + 4 Combine like terms: -32 + 4 = -28 4 + 4x + x2 = -28 Factor a perfect square on the left side: (x + 2)(x + 2) = -28 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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