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Simplifying -16x2 + 96x + -576 = 0 Reorder the terms: -576 + 96x + -16x2 = 0 Solving -576 + 96x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(-36 + 6x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-36 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying -36 + 6x + -1x2 = 0 Solving -36 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 36 + -6x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -6x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -6x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -6x + x2 = 0 + -36 -6x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -6x + x2 = -36 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 = -36 + 9 Reorder the terms: 9 + -6x + x2 = -36 + 9 Combine like terms: -36 + 9 = -27 9 + -6x + x2 = -27 Factor a perfect square on the left side: (x + -3)(x + -3) = -27 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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