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Simplifying x = x2 + 7x + 12 Reorder the terms: x = 12 + 7x + x2 Solving x = 12 + 7x + x2 Solving for variable 'x'. Reorder the terms: -12 + x + -7x + -1x2 = 12 + 7x + x2 + -12 + -7x + -1x2 Combine like terms: x + -7x = -6x -12 + -6x + -1x2 = 12 + 7x + x2 + -12 + -7x + -1x2 Reorder the terms: -12 + -6x + -1x2 = 12 + -12 + 7x + -7x + x2 + -1x2 Combine like terms: 12 + -12 = 0 -12 + -6x + -1x2 = 0 + 7x + -7x + x2 + -1x2 -12 + -6x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 -12 + -6x + -1x2 = 0 + x2 + -1x2 -12 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 6x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 6x + x2)' equal to zero and attempt to solve: Simplifying 12 + 6x + x2 = 0 Solving 12 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 6x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 6x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 6x + x2 = 0 + -12 6x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 6x + x2 = -12 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -12 + 9 Reorder the terms: 9 + 6x + x2 = -12 + 9 Combine like terms: -12 + 9 = -3 9 + 6x + x2 = -3 Factor a perfect square on the left side: (x + 3)(x + 3) = -3 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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