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Simplifying 32x2 + -128x + 240 = 0 Reorder the terms: 240 + -128x + 32x2 = 0 Solving 240 + -128x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(15 + -8x + 2x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(15 + -8x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + -8x + 2x2 = 0 Solving 15 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -4x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -4x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -4x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -4x + x2 = 0 + -7.5 -4x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -4x + x2 = -7.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -7.5 + 4 Reorder the terms: 4 + -4x + x2 = -7.5 + 4 Combine like terms: -7.5 + 4 = -3.5 4 + -4x + x2 = -3.5 Factor a perfect square on the left side: (x + -2)(x + -2) = -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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