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Simplifying 2m2 + 4m + -100 = 0 Reorder the terms: -100 + 4m + 2m2 = 0 Solving -100 + 4m + 2m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 2m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 2m + m2)' equal to zero and attempt to solve: Simplifying -50 + 2m + m2 = 0 Solving -50 + 2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 2m + 50 + m2 = 0 + 50 Reorder the terms: -50 + 50 + 2m + m2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 2m + m2 = 0 + 50 2m + m2 = 0 + 50 Combine like terms: 0 + 50 = 50 2m + m2 = 50 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 = 50 + 1 Reorder the terms: 1 + 2m + m2 = 50 + 1 Combine like terms: 50 + 1 = 51 1 + 2m + m2 = 51 Factor a perfect square on the left side: (m + 1)(m + 1) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (m + 1) equal to 7.141428429 and -7.141428429.Subproblem 1
m + 1 = 7.141428429 Simplifying m + 1 = 7.141428429 Reorder the terms: 1 + m = 7.141428429 Solving 1 + m = 7.141428429 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 = 7.141428429 + -1 Combine like terms: 1 + -1 = 0 0 + m = 7.141428429 + -1 m = 7.141428429 + -1 Combine like terms: 7.141428429 + -1 = 6.141428429 m = 6.141428429 Simplifying m = 6.141428429Subproblem 2
m + 1 = -7.141428429 Simplifying m + 1 = -7.141428429 Reorder the terms: 1 + m = -7.141428429 Solving 1 + m = -7.141428429 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 = -7.141428429 + -1 Combine like terms: 1 + -1 = 0 0 + m = -7.141428429 + -1 m = -7.141428429 + -1 Combine like terms: -7.141428429 + -1 = -8.141428429 m = -8.141428429 Simplifying m = -8.141428429Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.141428429, -8.141428429}Solution
m = {6.141428429, -8.141428429}
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