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Simplifying 2x2 + 100x + 3600 = 0 Reorder the terms: 3600 + 100x + 2x2 = 0 Solving 3600 + 100x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1800 + 50x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1800 + 50x + x2)' equal to zero and attempt to solve: Simplifying 1800 + 50x + x2 = 0 Solving 1800 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1800' to each side of the equation. 1800 + 50x + -1800 + x2 = 0 + -1800 Reorder the terms: 1800 + -1800 + 50x + x2 = 0 + -1800 Combine like terms: 1800 + -1800 = 0 0 + 50x + x2 = 0 + -1800 50x + x2 = 0 + -1800 Combine like terms: 0 + -1800 = -1800 50x + x2 = -1800 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = -1800 + 625 Reorder the terms: 625 + 50x + x2 = -1800 + 625 Combine like terms: -1800 + 625 = -1175 625 + 50x + x2 = -1175 Factor a perfect square on the left side: (x + 25)(x + 25) = -1175 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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