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Simplifying m2 + 4m = 47 Reorder the terms: 4m + m2 = 47 Solving 4m + m2 = 47 Solving for variable 'm'. Reorder the terms: -47 + 4m + m2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + 4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 4m + 47 + m2 = 0 + 47 Reorder the terms: -47 + 47 + 4m + m2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 4m + m2 = 0 + 47 4m + m2 = 0 + 47 Combine like terms: 0 + 47 = 47 4m + m2 = 47 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 = 47 + 4 Reorder the terms: 4 + 4m + m2 = 47 + 4 Combine like terms: 47 + 4 = 51 4 + 4m + m2 = 51 Factor a perfect square on the left side: (m + 2)(m + 2) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (m + 2) equal to 7.141428429 and -7.141428429.Subproblem 1
m + 2 = 7.141428429 Simplifying m + 2 = 7.141428429 Reorder the terms: 2 + m = 7.141428429 Solving 2 + m = 7.141428429 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 = 7.141428429 + -2 Combine like terms: 2 + -2 = 0 0 + m = 7.141428429 + -2 m = 7.141428429 + -2 Combine like terms: 7.141428429 + -2 = 5.141428429 m = 5.141428429 Simplifying m = 5.141428429Subproblem 2
m + 2 = -7.141428429 Simplifying m + 2 = -7.141428429 Reorder the terms: 2 + m = -7.141428429 Solving 2 + m = -7.141428429 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 = -7.141428429 + -2 Combine like terms: 2 + -2 = 0 0 + m = -7.141428429 + -2 m = -7.141428429 + -2 Combine like terms: -7.141428429 + -2 = -9.141428429 m = -9.141428429 Simplifying m = -9.141428429Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.141428429, -9.141428429}
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