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Simplifying 3m2 = 21 + 6m Solving 3m2 = 21 + 6m Solving for variable 'm'. Reorder the terms: -21 + -6m + 3m2 = 21 + 6m + -21 + -6m Reorder the terms: -21 + -6m + 3m2 = 21 + -21 + 6m + -6m Combine like terms: 21 + -21 = 0 -21 + -6m + 3m2 = 0 + 6m + -6m -21 + -6m + 3m2 = 6m + -6m Combine like terms: 6m + -6m = 0 -21 + -6m + 3m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + -2m + m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -2m + m2)' equal to zero and attempt to solve: Simplifying -7 + -2m + m2 = 0 Solving -7 + -2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -2m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + -2m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2m + m2 = 0 + 7 -2m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 -2m + m2 = 7 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 7 + 1 Reorder the terms: 1 + -2m + m2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + -2m + m2 = 8 Factor a perfect square on the left side: (m + -1)(m + -1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (m + -1) equal to 2.828427125 and -2.828427125.Subproblem 1
m + -1 = 2.828427125 Simplifying m + -1 = 2.828427125 Reorder the terms: -1 + m = 2.828427125 Solving -1 + m = 2.828427125 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + m = 2.828427125 + 1 m = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 m = 3.828427125 Simplifying m = 3.828427125Subproblem 2
m + -1 = -2.828427125 Simplifying m + -1 = -2.828427125 Reorder the terms: -1 + m = -2.828427125 Solving -1 + m = -2.828427125 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + m = -2.828427125 + 1 m = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 m = -1.828427125 Simplifying m = -1.828427125Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.828427125, -1.828427125}Solution
m = {3.828427125, -1.828427125}
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