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Simplifying 4x2 + -32x + 78 = 0 Reorder the terms: 78 + -32x + 4x2 = 0 Solving 78 + -32x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(39 + -16x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(39 + -16x + 2x2)' equal to zero and attempt to solve: Simplifying 39 + -16x + 2x2 = 0 Solving 39 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 19.5 + -8x + x2 = 0 Move the constant term to the right: Add '-19.5' to each side of the equation. 19.5 + -8x + -19.5 + x2 = 0 + -19.5 Reorder the terms: 19.5 + -19.5 + -8x + x2 = 0 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + -8x + x2 = 0 + -19.5 -8x + x2 = 0 + -19.5 Combine like terms: 0 + -19.5 = -19.5 -8x + x2 = -19.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -19.5 + 16 Reorder the terms: 16 + -8x + x2 = -19.5 + 16 Combine like terms: -19.5 + 16 = -3.5 16 + -8x + x2 = -3.5 Factor a perfect square on the left side: (x + -4)(x + -4) = -3.5 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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