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Simplifying m(m) + 12m + -35 = 0 Multiply m * m m2 + 12m + -35 = 0 Reorder the terms: -35 + 12m + m2 = 0 Solving -35 + 12m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 12m + 35 + m2 = 0 + 35 Reorder the terms: -35 + 35 + 12m + m2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 12m + m2 = 0 + 35 12m + m2 = 0 + 35 Combine like terms: 0 + 35 = 35 12m + m2 = 35 The m term is 12m. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12m + 36 + m2 = 35 + 36 Reorder the terms: 36 + 12m + m2 = 35 + 36 Combine like terms: 35 + 36 = 71 36 + 12m + m2 = 71 Factor a perfect square on the left side: (m + 6)(m + 6) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (m + 6) equal to 8.426149773 and -8.426149773.Subproblem 1
m + 6 = 8.426149773 Simplifying m + 6 = 8.426149773 Reorder the terms: 6 + m = 8.426149773 Solving 6 + m = 8.426149773 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + m = 8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + m = 8.426149773 + -6 m = 8.426149773 + -6 Combine like terms: 8.426149773 + -6 = 2.426149773 m = 2.426149773 Simplifying m = 2.426149773Subproblem 2
m + 6 = -8.426149773 Simplifying m + 6 = -8.426149773 Reorder the terms: 6 + m = -8.426149773 Solving 6 + m = -8.426149773 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + m = -8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + m = -8.426149773 + -6 m = -8.426149773 + -6 Combine like terms: -8.426149773 + -6 = -14.426149773 m = -14.426149773 Simplifying m = -14.426149773Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.426149773, -14.426149773}
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