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Simplifying (-51 + -13m) * m = 13 Reorder the terms for easier multiplication: m(-51 + -13m) = 13 (-51 * m + -13m * m) = 13 (-51m + -13m2) = 13 Solving -51m + -13m2 = 13 Solving for variable 'm'. Reorder the terms: -13 + -51m + -13m2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -51m + -13m2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 51m + 13m2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 51m + 13m2)' equal to zero and attempt to solve: Simplifying 13 + 51m + 13m2 = 0 Solving 13 + 51m + 13m2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 1 + 3.923076923m + m2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3.923076923m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + 3.923076923m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3.923076923m + m2 = 0 + -1 3.923076923m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 3.923076923m + m2 = -1 The m term is 3.923076923m. Take half its coefficient (1.961538462). Square it (3.847633138) and add it to both sides. Add '3.847633138' to each side of the equation. 3.923076923m + 3.847633138 + m2 = -1 + 3.847633138 Reorder the terms: 3.847633138 + 3.923076923m + m2 = -1 + 3.847633138 Combine like terms: -1 + 3.847633138 = 2.847633138 3.847633138 + 3.923076923m + m2 = 2.847633138 Factor a perfect square on the left side: (m + 1.961538462)(m + 1.961538462) = 2.847633138 Calculate the square root of the right side: 1.687493152 Break this problem into two subproblems by setting (m + 1.961538462) equal to 1.687493152 and -1.687493152.Subproblem 1
m + 1.961538462 = 1.687493152 Simplifying m + 1.961538462 = 1.687493152 Reorder the terms: 1.961538462 + m = 1.687493152 Solving 1.961538462 + m = 1.687493152 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.961538462' to each side of the equation. 1.961538462 + -1.961538462 + m = 1.687493152 + -1.961538462 Combine like terms: 1.961538462 + -1.961538462 = 0.000000000 0.000000000 + m = 1.687493152 + -1.961538462 m = 1.687493152 + -1.961538462 Combine like terms: 1.687493152 + -1.961538462 = -0.27404531 m = -0.27404531 Simplifying m = -0.27404531Subproblem 2
m + 1.961538462 = -1.687493152 Simplifying m + 1.961538462 = -1.687493152 Reorder the terms: 1.961538462 + m = -1.687493152 Solving 1.961538462 + m = -1.687493152 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.961538462' to each side of the equation. 1.961538462 + -1.961538462 + m = -1.687493152 + -1.961538462 Combine like terms: 1.961538462 + -1.961538462 = 0.000000000 0.000000000 + m = -1.687493152 + -1.961538462 m = -1.687493152 + -1.961538462 Combine like terms: -1.687493152 + -1.961538462 = -3.649031614 m = -3.649031614 Simplifying m = -3.649031614Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.27404531, -3.649031614}Solution
m = {-0.27404531, -3.649031614}
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