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Simplifying m2 + 5m + -13 = -4 Reorder the terms: -13 + 5m + m2 = -4 Solving -13 + 5m + m2 = -4 Solving for variable 'm'. Reorder the terms: -13 + 4 + 5m + m2 = -4 + 4 Combine like terms: -13 + 4 = -9 -9 + 5m + m2 = -4 + 4 Combine like terms: -4 + 4 = 0 -9 + 5m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 5m + 9 + m2 = 0 + 9 Reorder the terms: -9 + 9 + 5m + m2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5m + m2 = 0 + 9 5m + m2 = 0 + 9 Combine like terms: 0 + 9 = 9 5m + m2 = 9 The m term is 5m. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5m + 6.25 + m2 = 9 + 6.25 Reorder the terms: 6.25 + 5m + m2 = 9 + 6.25 Combine like terms: 9 + 6.25 = 15.25 6.25 + 5m + m2 = 15.25 Factor a perfect square on the left side: (m + 2.5)(m + 2.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (m + 2.5) equal to 3.905124838 and -3.905124838.Subproblem 1
m + 2.5 = 3.905124838 Simplifying m + 2.5 = 3.905124838 Reorder the terms: 2.5 + m = 3.905124838 Solving 2.5 + m = 3.905124838 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = 3.905124838 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = 3.905124838 + -2.5 m = 3.905124838 + -2.5 Combine like terms: 3.905124838 + -2.5 = 1.405124838 m = 1.405124838 Simplifying m = 1.405124838Subproblem 2
m + 2.5 = -3.905124838 Simplifying m + 2.5 = -3.905124838 Reorder the terms: 2.5 + m = -3.905124838 Solving 2.5 + m = -3.905124838 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = -3.905124838 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = -3.905124838 + -2.5 m = -3.905124838 + -2.5 Combine like terms: -3.905124838 + -2.5 = -6.405124838 m = -6.405124838 Simplifying m = -6.405124838Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.405124838, -6.405124838}
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