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Simplifying -13 = 5(1 + 4m) * 2m Reorder the terms for easier multiplication: -13 = 5 * 2m(1 + 4m) Multiply 5 * 2 -13 = 10m(1 + 4m) -13 = (1 * 10m + 4m * 10m) -13 = (10m + 40m2) Solving -13 = 10m + 40m2 Solving for variable 'm'. Reorder the terms: -13 + -10m + -40m2 = 10m + -10m + 40m2 + -40m2 Combine like terms: 10m + -10m = 0 -13 + -10m + -40m2 = 0 + 40m2 + -40m2 -13 + -10m + -40m2 = 40m2 + -40m2 Combine like terms: 40m2 + -40m2 = 0 -13 + -10m + -40m2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 10m + 40m2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 10m + 40m2)' equal to zero and attempt to solve: Simplifying 13 + 10m + 40m2 = 0 Solving 13 + 10m + 40m2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.325 + 0.25m + m2 = 0.0 Move the constant term to the right: Add '-0.325' to each side of the equation. 0.325 + 0.25m + -0.325 + m2 = 0.0 + -0.325 Reorder the terms: 0.325 + -0.325 + 0.25m + m2 = 0.0 + -0.325 Combine like terms: 0.325 + -0.325 = 0.000 0.000 + 0.25m + m2 = 0.0 + -0.325 0.25m + m2 = 0.0 + -0.325 Combine like terms: 0.0 + -0.325 = -0.325 0.25m + m2 = -0.325 The m term is 0.25m. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25m + 0.015625 + m2 = -0.325 + 0.015625 Reorder the terms: 0.015625 + 0.25m + m2 = -0.325 + 0.015625 Combine like terms: -0.325 + 0.015625 = -0.309375 0.015625 + 0.25m + m2 = -0.309375 Factor a perfect square on the left side: (m + 0.125)(m + 0.125) = -0.309375 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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