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Simplifying 90x2 + -370x + 3600 = 96 Reorder the terms: 3600 + -370x + 90x2 = 96 Solving 3600 + -370x + 90x2 = 96 Solving for variable 'x'. Reorder the terms: 3600 + -96 + -370x + 90x2 = 96 + -96 Combine like terms: 3600 + -96 = 3504 3504 + -370x + 90x2 = 96 + -96 Combine like terms: 96 + -96 = 0 3504 + -370x + 90x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1752 + -185x + 45x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1752 + -185x + 45x2)' equal to zero and attempt to solve: Simplifying 1752 + -185x + 45x2 = 0 Solving 1752 + -185x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. 38.93333333 + -4.111111111x + x2 = 0 Move the constant term to the right: Add '-38.93333333' to each side of the equation. 38.93333333 + -4.111111111x + -38.93333333 + x2 = 0 + -38.93333333 Reorder the terms: 38.93333333 + -38.93333333 + -4.111111111x + x2 = 0 + -38.93333333 Combine like terms: 38.93333333 + -38.93333333 = 0.00000000 0.00000000 + -4.111111111x + x2 = 0 + -38.93333333 -4.111111111x + x2 = 0 + -38.93333333 Combine like terms: 0 + -38.93333333 = -38.93333333 -4.111111111x + x2 = -38.93333333 The x term is -4.111111111x. Take half its coefficient (-2.055555556). Square it (4.225308644) and add it to both sides. Add '4.225308644' to each side of the equation. -4.111111111x + 4.225308644 + x2 = -38.93333333 + 4.225308644 Reorder the terms: 4.225308644 + -4.111111111x + x2 = -38.93333333 + 4.225308644 Combine like terms: -38.93333333 + 4.225308644 = -34.708024686 4.225308644 + -4.111111111x + x2 = -34.708024686 Factor a perfect square on the left side: (x + -2.055555556)(x + -2.055555556) = -34.708024686 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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