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Simplifying 0 = 54 + 6x + x2 Solving 0 = 54 + 6x + x2 Solving for variable 'x'. Combine like terms: 0 + -54 = -54 -54 + -6x + -1x2 = 54 + 6x + x2 + -54 + -6x + -1x2 Reorder the terms: -54 + -6x + -1x2 = 54 + -54 + 6x + -6x + x2 + -1x2 Combine like terms: 54 + -54 = 0 -54 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 -54 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -54 + -6x + -1x2 = 0 + x2 + -1x2 -54 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -54 + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(54 + 6x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(54 + 6x + x2)' equal to zero and attempt to solve: Simplifying 54 + 6x + x2 = 0 Solving 54 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + 6x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + 6x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + 6x + x2 = 0 + -54 6x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 6x + x2 = -54 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 = -54 + 9 Reorder the terms: 9 + 6x + x2 = -54 + 9 Combine like terms: -54 + 9 = -45 9 + 6x + x2 = -45 Factor a perfect square on the left side: (x + 3)(x + 3) = -45 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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