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Simplifying m2 + -5m + -4 = 0 Reorder the terms: -4 + -5m + m2 = 0 Solving -4 + -5m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -5m + 4 + m2 = 0 + 4 Reorder the terms: -4 + 4 + -5m + m2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5m + m2 = 0 + 4 -5m + m2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5m + m2 = 4 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 = 4 + 6.25 Reorder the terms: 6.25 + -5m + m2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5m + m2 = 10.25 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (m + -2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
m + -2.5 = 3.201562119 Simplifying m + -2.5 = 3.201562119 Reorder the terms: -2.5 + m = 3.201562119 Solving -2.5 + m = 3.201562119 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 = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 3.201562119 + 2.5 m = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 m = 5.701562119 Simplifying m = 5.701562119Subproblem 2
m + -2.5 = -3.201562119 Simplifying m + -2.5 = -3.201562119 Reorder the terms: -2.5 + m = -3.201562119 Solving -2.5 + m = -3.201562119 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 = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -3.201562119 + 2.5 m = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 m = -0.701562119 Simplifying m = -0.701562119Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.701562119, -0.701562119}
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