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Simplifying 2x2 + 12x + 66 = 0 Reorder the terms: 66 + 12x + 2x2 = 0 Solving 66 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(33 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(33 + 6x + x2)' equal to zero and attempt to solve: Simplifying 33 + 6x + x2 = 0 Solving 33 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + 6x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + 6x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 6x + x2 = 0 + -33 6x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 6x + x2 = -33 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 = -33 + 9 Reorder the terms: 9 + 6x + x2 = -33 + 9 Combine like terms: -33 + 9 = -24 9 + 6x + x2 = -24 Factor a perfect square on the left side: (x + 3)(x + 3) = -24 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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