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Simplifying m2 + 11m + 21 = 0 Reorder the terms: 21 + 11m + m2 = 0 Solving 21 + 11m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 11m + -21 + m2 = 0 + -21 Reorder the terms: 21 + -21 + 11m + m2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 11m + m2 = 0 + -21 11m + m2 = 0 + -21 Combine like terms: 0 + -21 = -21 11m + m2 = -21 The m term is 11m. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11m + 30.25 + m2 = -21 + 30.25 Reorder the terms: 30.25 + 11m + m2 = -21 + 30.25 Combine like terms: -21 + 30.25 = 9.25 30.25 + 11m + m2 = 9.25 Factor a perfect square on the left side: (m + 5.5)(m + 5.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (m + 5.5) equal to 3.041381265 and -3.041381265.Subproblem 1
m + 5.5 = 3.041381265 Simplifying m + 5.5 = 3.041381265 Reorder the terms: 5.5 + m = 3.041381265 Solving 5.5 + m = 3.041381265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + m = 3.041381265 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + m = 3.041381265 + -5.5 m = 3.041381265 + -5.5 Combine like terms: 3.041381265 + -5.5 = -2.458618735 m = -2.458618735 Simplifying m = -2.458618735Subproblem 2
m + 5.5 = -3.041381265 Simplifying m + 5.5 = -3.041381265 Reorder the terms: 5.5 + m = -3.041381265 Solving 5.5 + m = -3.041381265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + m = -3.041381265 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + m = -3.041381265 + -5.5 m = -3.041381265 + -5.5 Combine like terms: -3.041381265 + -5.5 = -8.541381265 m = -8.541381265 Simplifying m = -8.541381265Solution
The solution to the problem is based on the solutions from the subproblems. m = {-2.458618735, -8.541381265}
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