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Simplifying 1m2 + 9m + -5 = 0 Reorder the terms: -5 + 9m + 1m2 = 0 Solving -5 + 9m + 1m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 9m + 5 + m2 = 0 + 5 Reorder the terms: -5 + 5 + 9m + m2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 9m + m2 = 0 + 5 9m + m2 = 0 + 5 Combine like terms: 0 + 5 = 5 9m + m2 = 5 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 = 5 + 20.25 Reorder the terms: 20.25 + 9m + m2 = 5 + 20.25 Combine like terms: 5 + 20.25 = 25.25 20.25 + 9m + m2 = 25.25 Factor a perfect square on the left side: (m + 4.5)(m + 4.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (m + 4.5) equal to 5.024937811 and -5.024937811.Subproblem 1
m + 4.5 = 5.024937811 Simplifying m + 4.5 = 5.024937811 Reorder the terms: 4.5 + m = 5.024937811 Solving 4.5 + m = 5.024937811 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 = 5.024937811 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + m = 5.024937811 + -4.5 m = 5.024937811 + -4.5 Combine like terms: 5.024937811 + -4.5 = 0.524937811 m = 0.524937811 Simplifying m = 0.524937811Subproblem 2
m + 4.5 = -5.024937811 Simplifying m + 4.5 = -5.024937811 Reorder the terms: 4.5 + m = -5.024937811 Solving 4.5 + m = -5.024937811 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 = -5.024937811 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + m = -5.024937811 + -4.5 m = -5.024937811 + -4.5 Combine like terms: -5.024937811 + -4.5 = -9.524937811 m = -9.524937811 Simplifying m = -9.524937811Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.524937811, -9.524937811}
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