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Simplifying 0 = 36x2 + -8x + 128 Reorder the terms: 0 = 128 + -8x + 36x2 Solving 0 = 128 + -8x + 36x2 Solving for variable 'x'. Combine like terms: 0 + -128 = -128 -128 + 8x + -36x2 = 128 + -8x + 36x2 + -128 + 8x + -36x2 Reorder the terms: -128 + 8x + -36x2 = 128 + -128 + -8x + 8x + 36x2 + -36x2 Combine like terms: 128 + -128 = 0 -128 + 8x + -36x2 = 0 + -8x + 8x + 36x2 + -36x2 -128 + 8x + -36x2 = -8x + 8x + 36x2 + -36x2 Combine like terms: -8x + 8x = 0 -128 + 8x + -36x2 = 0 + 36x2 + -36x2 -128 + 8x + -36x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 -128 + 8x + -36x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-32 + 2x + -9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-32 + 2x + -9x2)' equal to zero and attempt to solve: Simplifying -32 + 2x + -9x2 = 0 Solving -32 + 2x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 3.555555556 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '-3.555555556' to each side of the equation. 3.555555556 + -0.2222222222x + -3.555555556 + x2 = 0 + -3.555555556 Reorder the terms: 3.555555556 + -3.555555556 + -0.2222222222x + x2 = 0 + -3.555555556 Combine like terms: 3.555555556 + -3.555555556 = 0.000000000 0.000000000 + -0.2222222222x + x2 = 0 + -3.555555556 -0.2222222222x + x2 = 0 + -3.555555556 Combine like terms: 0 + -3.555555556 = -3.555555556 -0.2222222222x + x2 = -3.555555556 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = -3.555555556 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = -3.555555556 + 0.01234567901 Combine like terms: -3.555555556 + 0.01234567901 = -3.54320987699 0.01234567901 + -0.2222222222x + x2 = -3.54320987699 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = -3.54320987699 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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