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Simplifying 500 = 45m + 35m(12 + -35m) 500 = 45m + (12 * 35m + -35m * 35m) 500 = 45m + (420m + -1225m2) Combine like terms: 45m + 420m = 465m 500 = 465m + -1225m2 Solving 500 = 465m + -1225m2 Solving for variable 'm'. Reorder the terms: 500 + -465m + 1225m2 = 465m + -465m + -1225m2 + 1225m2 Combine like terms: 465m + -465m = 0 500 + -465m + 1225m2 = 0 + -1225m2 + 1225m2 500 + -465m + 1225m2 = -1225m2 + 1225m2 Combine like terms: -1225m2 + 1225m2 = 0 500 + -465m + 1225m2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(100 + -93m + 245m2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(100 + -93m + 245m2)' equal to zero and attempt to solve: Simplifying 100 + -93m + 245m2 = 0 Solving 100 + -93m + 245m2 = 0 Begin completing the square. Divide all terms by 245 the coefficient of the squared term: Divide each side by '245'. 0.4081632653 + -0.3795918367m + m2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.3795918367m + -0.4081632653 + m2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -0.3795918367m + m2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -0.3795918367m + m2 = 0 + -0.4081632653 -0.3795918367m + m2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -0.3795918367m + m2 = -0.4081632653 The m term is -0.3795918367m. Take half its coefficient (-0.1897959184). Square it (0.03602249064) and add it to both sides. Add '0.03602249064' to each side of the equation. -0.3795918367m + 0.03602249064 + m2 = -0.4081632653 + 0.03602249064 Reorder the terms: 0.03602249064 + -0.3795918367m + m2 = -0.4081632653 + 0.03602249064 Combine like terms: -0.4081632653 + 0.03602249064 = -0.37214077466 0.03602249064 + -0.3795918367m + m2 = -0.37214077466 Factor a perfect square on the left side: (m + -0.1897959184)(m + -0.1897959184) = -0.37214077466 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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