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Simplifying m2 + 20m + -4 = 0 Reorder the terms: -4 + 20m + m2 = 0 Solving -4 + 20m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 20m + 4 + m2 = 0 + 4 Reorder the terms: -4 + 4 + 20m + m2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 20m + m2 = 0 + 4 20m + m2 = 0 + 4 Combine like terms: 0 + 4 = 4 20m + m2 = 4 The m term is 20m. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20m + 100 + m2 = 4 + 100 Reorder the terms: 100 + 20m + m2 = 4 + 100 Combine like terms: 4 + 100 = 104 100 + 20m + m2 = 104 Factor a perfect square on the left side: (m + 10)(m + 10) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (m + 10) equal to 10.198039027 and -10.198039027.Subproblem 1
m + 10 = 10.198039027 Simplifying m + 10 = 10.198039027 Reorder the terms: 10 + m = 10.198039027 Solving 10 + m = 10.198039027 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + m = 10.198039027 + -10 Combine like terms: 10 + -10 = 0 0 + m = 10.198039027 + -10 m = 10.198039027 + -10 Combine like terms: 10.198039027 + -10 = 0.198039027 m = 0.198039027 Simplifying m = 0.198039027Subproblem 2
m + 10 = -10.198039027 Simplifying m + 10 = -10.198039027 Reorder the terms: 10 + m = -10.198039027 Solving 10 + m = -10.198039027 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + m = -10.198039027 + -10 Combine like terms: 10 + -10 = 0 0 + m = -10.198039027 + -10 m = -10.198039027 + -10 Combine like terms: -10.198039027 + -10 = -20.198039027 m = -20.198039027 Simplifying m = -20.198039027Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.198039027, -20.198039027}
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