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Simplifying 300x + -200x2 + -968080 = 300x2 + 12 Reorder the terms: -968080 + 300x + -200x2 = 300x2 + 12 Reorder the terms: -968080 + 300x + -200x2 = 12 + 300x2 Solving -968080 + 300x + -200x2 = 12 + 300x2 Solving for variable 'x'. Reorder the terms: -968080 + -12 + 300x + -200x2 + -300x2 = 12 + 300x2 + -12 + -300x2 Combine like terms: -968080 + -12 = -968092 -968092 + 300x + -200x2 + -300x2 = 12 + 300x2 + -12 + -300x2 Combine like terms: -200x2 + -300x2 = -500x2 -968092 + 300x + -500x2 = 12 + 300x2 + -12 + -300x2 Reorder the terms: -968092 + 300x + -500x2 = 12 + -12 + 300x2 + -300x2 Combine like terms: 12 + -12 = 0 -968092 + 300x + -500x2 = 0 + 300x2 + -300x2 -968092 + 300x + -500x2 = 300x2 + -300x2 Combine like terms: 300x2 + -300x2 = 0 -968092 + 300x + -500x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-242023 + 75x + -125x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-242023 + 75x + -125x2)' equal to zero and attempt to solve: Simplifying -242023 + 75x + -125x2 = 0 Solving -242023 + 75x + -125x2 = 0 Begin completing the square. Divide all terms by -125 the coefficient of the squared term: Divide each side by '-125'. 1936.184 + -0.6x + x2 = 0 Move the constant term to the right: Add '-1936.184' to each side of the equation. 1936.184 + -0.6x + -1936.184 + x2 = 0 + -1936.184 Reorder the terms: 1936.184 + -1936.184 + -0.6x + x2 = 0 + -1936.184 Combine like terms: 1936.184 + -1936.184 = 0.000 0.000 + -0.6x + x2 = 0 + -1936.184 -0.6x + x2 = 0 + -1936.184 Combine like terms: 0 + -1936.184 = -1936.184 -0.6x + x2 = -1936.184 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = -1936.184 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = -1936.184 + 0.09 Combine like terms: -1936.184 + 0.09 = -1936.094 0.09 + -0.6x + x2 = -1936.094 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = -1936.094 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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