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Simplifying m2 + 20m = -70 Reorder the terms: 20m + m2 = -70 Solving 20m + m2 = -70 Solving for variable 'm'. Reorder the terms: 70 + 20m + m2 = -70 + 70 Combine like terms: -70 + 70 = 0 70 + 20m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + 20m + -70 + m2 = 0 + -70 Reorder the terms: 70 + -70 + 20m + m2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + 20m + m2 = 0 + -70 20m + m2 = 0 + -70 Combine like terms: 0 + -70 = -70 20m + m2 = -70 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 = -70 + 100 Reorder the terms: 100 + 20m + m2 = -70 + 100 Combine like terms: -70 + 100 = 30 100 + 20m + m2 = 30 Factor a perfect square on the left side: (m + 10)(m + 10) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (m + 10) equal to 5.477225575 and -5.477225575.Subproblem 1
m + 10 = 5.477225575 Simplifying m + 10 = 5.477225575 Reorder the terms: 10 + m = 5.477225575 Solving 10 + m = 5.477225575 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 = 5.477225575 + -10 Combine like terms: 10 + -10 = 0 0 + m = 5.477225575 + -10 m = 5.477225575 + -10 Combine like terms: 5.477225575 + -10 = -4.522774425 m = -4.522774425 Simplifying m = -4.522774425Subproblem 2
m + 10 = -5.477225575 Simplifying m + 10 = -5.477225575 Reorder the terms: 10 + m = -5.477225575 Solving 10 + m = -5.477225575 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 = -5.477225575 + -10 Combine like terms: 10 + -10 = 0 0 + m = -5.477225575 + -10 m = -5.477225575 + -10 Combine like terms: -5.477225575 + -10 = -15.477225575 m = -15.477225575 Simplifying m = -15.477225575Solution
The solution to the problem is based on the solutions from the subproblems. m = {-4.522774425, -15.477225575}
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