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Simplifying -2m(m + 1) = 10 Reorder the terms: -2m(1 + m) = 10 (1 * -2m + m * -2m) = 10 (-2m + -2m2) = 10 Solving -2m + -2m2 = 10 Solving for variable 'm'. Reorder the terms: -10 + -2m + -2m2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -2m + -2m2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + m + m2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + m + m2)' equal to zero and attempt to solve: Simplifying 5 + m + m2 = 0 Solving 5 + m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + m + -5 + m2 = 0 + -5 Reorder the terms: 5 + -5 + m + m2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + m + m2 = 0 + -5 m + m2 = 0 + -5 Combine like terms: 0 + -5 = -5 m + m2 = -5 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. m + 0.25 + m2 = -5 + 0.25 Reorder the terms: 0.25 + m + m2 = -5 + 0.25 Combine like terms: -5 + 0.25 = -4.75 0.25 + m + m2 = -4.75 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = -4.75 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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