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Simplifying m2 + -44m + 74 = 0 Reorder the terms: 74 + -44m + m2 = 0 Solving 74 + -44m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-74' to each side of the equation. 74 + -44m + -74 + m2 = 0 + -74 Reorder the terms: 74 + -74 + -44m + m2 = 0 + -74 Combine like terms: 74 + -74 = 0 0 + -44m + m2 = 0 + -74 -44m + m2 = 0 + -74 Combine like terms: 0 + -74 = -74 -44m + m2 = -74 The m term is -44m. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44m + 484 + m2 = -74 + 484 Reorder the terms: 484 + -44m + m2 = -74 + 484 Combine like terms: -74 + 484 = 410 484 + -44m + m2 = 410 Factor a perfect square on the left side: (m + -22)(m + -22) = 410 Calculate the square root of the right side: 20.248456731 Break this problem into two subproblems by setting (m + -22) equal to 20.248456731 and -20.248456731.Subproblem 1
m + -22 = 20.248456731 Simplifying m + -22 = 20.248456731 Reorder the terms: -22 + m = 20.248456731 Solving -22 + m = 20.248456731 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + m = 20.248456731 + 22 Combine like terms: -22 + 22 = 0 0 + m = 20.248456731 + 22 m = 20.248456731 + 22 Combine like terms: 20.248456731 + 22 = 42.248456731 m = 42.248456731 Simplifying m = 42.248456731Subproblem 2
m + -22 = -20.248456731 Simplifying m + -22 = -20.248456731 Reorder the terms: -22 + m = -20.248456731 Solving -22 + m = -20.248456731 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + m = -20.248456731 + 22 Combine like terms: -22 + 22 = 0 0 + m = -20.248456731 + 22 m = -20.248456731 + 22 Combine like terms: -20.248456731 + 22 = 1.751543269 m = 1.751543269 Simplifying m = 1.751543269Solution
The solution to the problem is based on the solutions from the subproblems. m = {42.248456731, 1.751543269}
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