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Simplifying 4m(m + -4) = 16 Reorder the terms: 4m(-4 + m) = 16 (-4 * 4m + m * 4m) = 16 (-16m + 4m2) = 16 Solving -16m + 4m2 = 16 Solving for variable 'm'. Reorder the terms: -16 + -16m + 4m2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -16m + 4m2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -4m + m2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -4m + m2)' equal to zero and attempt to solve: Simplifying -4 + -4m + m2 = 0 Solving -4 + -4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -4m + 4 + m2 = 0 + 4 Reorder the terms: -4 + 4 + -4m + m2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4m + m2 = 0 + 4 -4m + m2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4m + m2 = 4 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 4 + 4 Reorder the terms: 4 + -4m + m2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4m + m2 = 8 Factor a perfect square on the left side: (m + -2)(m + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (m + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
m + -2 = 2.828427125 Simplifying m + -2 = 2.828427125 Reorder the terms: -2 + m = 2.828427125 Solving -2 + m = 2.828427125 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + m = 2.828427125 + 2 m = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 m = 4.828427125 Simplifying m = 4.828427125Subproblem 2
m + -2 = -2.828427125 Simplifying m + -2 = -2.828427125 Reorder the terms: -2 + m = -2.828427125 Solving -2 + m = -2.828427125 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + m = -2.828427125 + 2 m = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 m = -0.828427125 Simplifying m = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.828427125, -0.828427125}Solution
m = {4.828427125, -0.828427125}
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