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Simplifying 45x * 45x + 240x + 180 = 0 Reorder the terms for easier multiplication: 45 * 45x * x + 240x + 180 = 0 Multiply 45 * 45 2025x * x + 240x + 180 = 0 Multiply x * x 2025x2 + 240x + 180 = 0 Reorder the terms: 180 + 240x + 2025x2 = 0 Solving 180 + 240x + 2025x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '15'. 15(12 + 16x + 135x2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(12 + 16x + 135x2)' equal to zero and attempt to solve: Simplifying 12 + 16x + 135x2 = 0 Solving 12 + 16x + 135x2 = 0 Begin completing the square. Divide all terms by 135 the coefficient of the squared term: Divide each side by '135'. 0.08888888889 + 0.1185185185x + x2 = 0 Move the constant term to the right: Add '-0.08888888889' to each side of the equation. 0.08888888889 + 0.1185185185x + -0.08888888889 + x2 = 0 + -0.08888888889 Reorder the terms: 0.08888888889 + -0.08888888889 + 0.1185185185x + x2 = 0 + -0.08888888889 Combine like terms: 0.08888888889 + -0.08888888889 = 0.00000000000 0.00000000000 + 0.1185185185x + x2 = 0 + -0.08888888889 0.1185185185x + x2 = 0 + -0.08888888889 Combine like terms: 0 + -0.08888888889 = -0.08888888889 0.1185185185x + x2 = -0.08888888889 The x term is 0.1185185185x. Take half its coefficient (0.05925925925). Square it (0.003511659807) and add it to both sides. Add '0.003511659807' to each side of the equation. 0.1185185185x + 0.003511659807 + x2 = -0.08888888889 + 0.003511659807 Reorder the terms: 0.003511659807 + 0.1185185185x + x2 = -0.08888888889 + 0.003511659807 Combine like terms: -0.08888888889 + 0.003511659807 = -0.085377229083 0.003511659807 + 0.1185185185x + x2 = -0.085377229083 Factor a perfect square on the left side: (x + 0.05925925925)(x + 0.05925925925) = -0.085377229083 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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