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Simplifying m2 + 9m = 14 Reorder the terms: 9m + m2 = 14 Solving 9m + m2 = 14 Solving for variable 'm'. Reorder the terms: -14 + 9m + m2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 9m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 9m + 14 + m2 = 0 + 14 Reorder the terms: -14 + 14 + 9m + m2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 9m + m2 = 0 + 14 9m + m2 = 0 + 14 Combine like terms: 0 + 14 = 14 9m + m2 = 14 The m term is 9m. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9m + 20.25 + m2 = 14 + 20.25 Reorder the terms: 20.25 + 9m + m2 = 14 + 20.25 Combine like terms: 14 + 20.25 = 34.25 20.25 + 9m + m2 = 34.25 Factor a perfect square on the left side: (m + 4.5)(m + 4.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (m + 4.5) equal to 5.852349955 and -5.852349955.Subproblem 1
m + 4.5 = 5.852349955 Simplifying m + 4.5 = 5.852349955 Reorder the terms: 4.5 + m = 5.852349955 Solving 4.5 + m = 5.852349955 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + m = 5.852349955 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + m = 5.852349955 + -4.5 m = 5.852349955 + -4.5 Combine like terms: 5.852349955 + -4.5 = 1.352349955 m = 1.352349955 Simplifying m = 1.352349955Subproblem 2
m + 4.5 = -5.852349955 Simplifying m + 4.5 = -5.852349955 Reorder the terms: 4.5 + m = -5.852349955 Solving 4.5 + m = -5.852349955 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + m = -5.852349955 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + m = -5.852349955 + -4.5 m = -5.852349955 + -4.5 Combine like terms: -5.852349955 + -4.5 = -10.352349955 m = -10.352349955 Simplifying m = -10.352349955Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.352349955, -10.352349955}
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