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Simplifying 4x2 + -24x + 81 = 3 Reorder the terms: 81 + -24x + 4x2 = 3 Solving 81 + -24x + 4x2 = 3 Solving for variable 'x'. Reorder the terms: 81 + -3 + -24x + 4x2 = 3 + -3 Combine like terms: 81 + -3 = 78 78 + -24x + 4x2 = 3 + -3 Combine like terms: 3 + -3 = 0 78 + -24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(39 + -12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(39 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying 39 + -12x + 2x2 = 0 Solving 39 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 19.5 + -6x + x2 = 0 Move the constant term to the right: Add '-19.5' to each side of the equation. 19.5 + -6x + -19.5 + x2 = 0 + -19.5 Reorder the terms: 19.5 + -19.5 + -6x + x2 = 0 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + -6x + x2 = 0 + -19.5 -6x + x2 = 0 + -19.5 Combine like terms: 0 + -19.5 = -19.5 -6x + x2 = -19.5 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 = -19.5 + 9 Reorder the terms: 9 + -6x + x2 = -19.5 + 9 Combine like terms: -19.5 + 9 = -10.5 9 + -6x + x2 = -10.5 Factor a perfect square on the left side: (x + -3)(x + -3) = -10.5 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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