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Simplifying -2x2 + -12x + -45 = 0 Reorder the terms: -45 + -12x + -2x2 = 0 Solving -45 + -12x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 12x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(45 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying 45 + 12x + 2x2 = 0 Solving 45 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + 6x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + 6x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + 6x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + 6x + x2 = 0 + -22.5 6x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 6x + x2 = -22.5 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 = -22.5 + 9 Reorder the terms: 9 + 6x + x2 = -22.5 + 9 Combine like terms: -22.5 + 9 = -13.5 9 + 6x + x2 = -13.5 Factor a perfect square on the left side: (x + 3)(x + 3) = -13.5 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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